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The coeff. of $x^n$ in the expansion of $(1+x)(1-x)^n$ is ?

$\begin{array}{1 1} (-1)^{n-1}.n \\ (-1)^{n}.(1-n) \\ (-1)^{n-1}.(n-1)^2 \\ (n-1) \end{array}$

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1 Answer

Coeff. of $x^n$ in the expansion $(1+x).(1-x)^n$ is
=$\big[$Coeff. of $x^n$ in $ (1-x)^n\big]+\big[$coeff. of $x^{n-1}$ in $(1-x)^n\big]$
$=(-1)^n.^nC_n+(-1)^{n-1}.^nC_{n-1}$
$=(-1)^n.(1-n)$
answered Oct 14, 2013 by rvidyagovindarajan_1
 

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