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Question

If the sum of n terms of the following series:

2n+12n1+3(2n+12n1)2+5(2n+12n1)3+is 36, then value of n is


A

2

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B

3

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C

4

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D

5

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Solution

The correct option is C

4


Putting x=2n+12n11x=22n1or x1x=(2n+12)LetS=x+3x2+5x3++(2n1)xnxS=x2+3x3++(2n3)xn+(2n1)xn+1–––––––––––––––––––––––––––––––––––––––––––––––––––S(1x)=x+[2x2+2x3++(n1) terms](2n1)xn+1=(2n+12)(2n)n(2n+1)=36 n=4


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