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Find the coefficient of x^n in the expan...

Find the coefficient of `x^n` in the expansion of `(1+x)(1+x)^ndot`

Text Solution

Verified by Experts

The correct Answer is:
`(-4)^(n) xx (n-1)`
`T_(r+1) " in " (1-x)^(n) = (-1)^(r+1) * .^(n) C_(r)* x^(r).`
`(1+x) (1-x)^(n) = (1+x) [ 1-.^(n)C_(1)x + ... + (-1)^(n) xx .^(n)C_(n-1) x^(n-1)+ (-1)^(n+1) *.^(n)C_(n)x^(n)].`
Coeff. Of `x^(n)` in the given product ` (1+x)(1-x) ^(n) = [(-1)^(n+1)* .^(n)C_(n) + (-1)^(n)*.^(n)C_(n-1)]`
`= (-1)^(n+1) + (-1)^(n) xx n = (-1)^(n) xx (n-1).`
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