If the sum of n terms of the following series-2 n-1-2 n-1-32 n-1-2 n-12-52 n-1-2 n-13- is 36- then value of n is

The correct option is C 4 Putting x=2n+1/2n 1 1 x= 2/2n 1 or x/1 x= ( 2n+1/2 ) Let S=x+3x^2+5x^3+… +(2n 1)x^n xS=x^2+3x^3+… + (2n 3)x^n+(2n 1)x^n+1 S(1 x) ...

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Standard XII

Mathematics

Sequence

If the sum of...

Question

If the sum of n terms of the following series:

$\frac{2 n + 1}{2 n - 1} + 3 {(\frac{2 n + 1}{2 n - 1})}^{2} + 5 {(\frac{2 n + 1}{2 n - 1})}^{3} + \dots$ is 36, then value of n is

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Solution

The correct option is C
4

Putting $x = \frac{2 n + 1}{2 n - 1} 1 - x = \frac{- 2}{2 n - 1} o r \frac{x}{1 - x} = - (\frac{2 n + 1}{2}) L e t S = x + 3 x^{2} + 5 x^{3} + \dots + (2 n - 1) x^{n} x S = x^{2} + 3 x^{3} + \dots + (2 n - 3) x^{n} + (2 n - 1) x^{n + 1} - --------------------------------------------------- - S (1 - x) = x + [2 x^{2} + 2 x^{3} + \dots + (n - 1) t e r m s] - (2 n - 1) x^{n + 1} = - (\frac{2 n + 1}{2}) (- 2 n) \Rightarrow n (2 n + 1) = 36 ∴ n = 4$

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If the sum of n terms of the following series: 2n+12n−1+3(2n+12n−1)2+5(2n+12n−1)3+…is 36, then value of n is

If the sum of n terms of the following series:

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