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If |x|<1, then find the coefficient of x...

If `|x|<1,` then find the coefficient of `x^n` in the expansion of `(1+x+x^2+......)^2dot`

A

n

B

n-1

C

n+2

D

n+1

Text Solution

Verified by Experts

The correct Answer is:
d
We have,
`( 1 + x + x^(2) + x^(3) + …)^(2), ` is We know that the coefficient `x^(n)` in `(1 - x)^(-r)` is `""^(n+r-1)C_(r -1)`.
So, coefficient of `x^(n)` in `(1 - x)^(-2) is ""^(n+ 2 -1)C_(2 -1) = ""^(n+1)C_(1) = n+1`
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  16. Find the following sum : (1)/(n!) + (1)/(2!(n-2)!) + (1)/(4!(n-4)!)+...

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