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Hello everyone.



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Welcome to the session.



3

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So today we will solve my problem with the help of the occasion.



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So the name of the problem is dramatic some ok do some genetic some.



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Now what is the problem so the problem is very simple.



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So given the value let's say the value of Case Three.



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So what we have to do we have to calculate the cities we have to convert the sum of our cities.



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Now the cities is very simple.



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So this will be the cities to the power too.



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And this is true to the poverty because the value of K Street.



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So I will go.



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So I will reach here.



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OK.



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One upon two to the power three basically in chart for a general key for a general cadence it is will



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look something like this when I bought two plus two square two cube and so on.



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One when two to the power game minus one.



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Then one upon two to the power key.



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Okay so we have to calculate the sum of the cities for a general key.



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Okay.



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The value of game will be given by the user.



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And this is how the cities will look like.



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So we have to use recursion to solve this problem.



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Okay so how we can use recursion to solve this problem.



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So what we will do we will break the series into okay.



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So this is basically true to the power about zero.



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Okay now we have a bigger problem.



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So with the help of the guys in what we will do we will give the smaller problem to that equation.



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So I will big the cities from here so if this total cities if I call it G some K so if I'm calling this



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total cities as geometric some K so what will the cities be called.



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So what is this series.



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So this series is nothing but this is geometric sum game minus 1.



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Okay so the equation will give me the answer for the cities okay.



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Recursion I believe recursion I believe the function equation will give me the answer for the cities.



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And after getting done I said what we will do I have to calculate this part.



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So this part is not a thing but it is just one divided by two.



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The power key so we can use the power function here.



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Power of the power key.



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Okay.



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And that is how we will get our answer.



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Okay so let us write the code now first of all before writing the code word we would answer for this



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when the value of case 3.



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So what do we answer.



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This will be one plus.



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So one by two.



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This is zero point five when by four.



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This will be zero point to five and then one by eight.



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So basically this will be zero point 1 2 5.



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So if we will add these four times we will get one point eight seven five.



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So basically our return type will be a double.



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Okay.



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This will be a double fluid.



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It will not be an integer.



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Okay now let us write the code and we will check.



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We will run our code against the value of equals 3.



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Okay so let's write the code



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so the return table will not be in digits sorry the return type will be double so I don't double double



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and let's say that maybe the function is geometric sum so GSM what it will take it will take a number



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as argument.



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Okay.



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So first of all base case we have to think about the base case.



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So if the value of k is 0 so what is the answer.



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If the value of k 0



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Okay so let's see again so if the value of k 0 is the value of case zero what is the cities.



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So the cities will be simply this one okay.



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For k equals zero I will say this will be one plus one divided by not one plus two to the power zero.



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Okay so this will be our city's fault because it'll This is our cities okay.



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For k was 3 so I will go till 3 when the value of k 0.



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I will go only this much okay.



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Only one time when the value of cake was you know I have only one item.



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So this is nothing but one by one.



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So this is one.



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Okay so what.



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This is our base case.



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If the value of KS is 0 I would answer this one.



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Okay.



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This is our base case so the value of Casey doing what I have to do.



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I have not done one.



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Now what do we do.



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Recursive case so the equation will give me the answer for the smaller problem.



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Okay so I will are done.



81

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I will store down in a double variable and so double small onset because the return type is double.



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So geometric sum



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I will give give minus 1 to domestic some will give me the dramatic sum of game minus one times and



84

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now the calculation but so the calculation part is very easy.



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What I have to do I have to calculate one thing.



86

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So I will return small answer plus.



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Now what we have to do we have to calculate this part okay.



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This is our last digit.



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So this is the last digit.



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This is the last digit.



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I have to calculate this last digit.



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So what I will do I will write when divided by two to the power key but this will be wrong because this



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is integer and this is in data and digit upon A.J. will be in Indonesia.



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But I want double value.



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Okay.



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So what I will do I will write one point zero.



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Okay so that I can get done so as double.



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So I will write to one point zero.



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So double up on it T.J. will be the one only.



100

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And then I am using powered function.



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So power function takes two things as argument.



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So I have to conclude it to the power key we can see here.



103

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I have to calculate to the power key okay.



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So this will be our code where the simple code.



105

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And now let us this double code let us call the G some function and later the value of Case 3 and 4



106

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3 we know the so should be one point eight seven five.



107

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Okay let's run our file so our answer is one point eighty seven five solver code is working fine.



108

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And if you want we can also do it.



109

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We can also died in our court.



110

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We can draw the diagram.



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So the value of case T okay so case not too close to zero.



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I will calculate.



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I will call the function for 2.



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Then I will call the function for 1.



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Then I will call the function for 0.



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So if the value of k 0 I am returning 1 so it will return 1.



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So basically the small answer contains 1 and then what I am doing I am calculating I am returning small



118

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answers I am returning small answer which is one plus one divided by 2 to the power key case one only.



119

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Okay so what I am returning so this is basically one plus this is zero point five.



120

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So basically one point five.



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So this answer for that sort so the smaller answer is one point five and then I am again small answer



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plus this part.



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So basically what I am returning I am returning when playing five plus one divided by two squared because



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the value of Case 2 so 1 divided by 4 when my 4.



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So what is 1 before.



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So when therefore is zero point to five.



127

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So one point five plus zero point two five so one point five plus point two five.



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So this will be five seven one point seven five.



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So the small answer is one point seven five.



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And then again the value of Case Three.



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So a small answer plus one by eight.



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And this will be one point eight seven five okay.



133

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So when by it is zero point twenty five.



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So if I will add one point seven five and zero point one two five.



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So this is five seven eight and one point eight seven five.



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So this is how that's how we will get our answer it will be one point eighty seven five.



137

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Okay.



138

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So I hope you understood this problem also.



139

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Okay so that 10 day will be double.



140

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And first we will write the code then we will think of the diagram.



141

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Okay then we will write and I will call it first.



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Write the code and then first write the code with the help of PMI and then draw the diagram.



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Okay.



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So I hope you understood this problem also.



145

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If you're having it out you can definitely ask me.



146

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Okay thank you.