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Find the sum to n terms of the series : ...

Find the sum to n terms of the series : `1+2x+3x^2+4x^3+......`

A

` 1/(1-x)`

B

`1/(1+x)`

C

`1/(1+x^(2))`

D

`1/(1+x)^(2)`

Text Solution

Verified by Experts

The correct Answer is:
d
Let = `+2 x +3x^(2) + 4x^(3) + …oo" "` …(i)
` x S = x + 2 x^(2) + 3x ^(3) + …oo" "` …(ii)
` (1-x)S = (1+x+x^(2) + … oo )`
` rArr S = 1/((1-x))(1/(1-x))=1/(1-x)^(2)`
Alternate Method
Here, a = 1, d = 1 , r = x
` :. S_(oo) = a/(1-r) +(d*r)/(1-r)^(2)=1/(1-x)+ (1*x)/(1-x)^(2)=1/((1-x)^(2))`
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