The correct matching of List I from List-II is :
The correct matching of List I from List-II is :
Solution
We know that
(a) $(1-x)^{-n}=1+n x+\frac{n(n+1)}{2 !} x^2+\ldots$ if $|x| < 1$
(b) $(1+x)^{-n}=1-n x+\frac{n(n+1)}{2 !} x^2-\ldots \quad$ if $|x| < 1$
(c) $1+\frac{1}{x}+\frac{1}{x^2}+\ldots \quad(\because x>1)$
$=\frac{1}{1-\frac{1}{x}}=\frac{x}{x-1}$
(d) $\quad 1-\frac{2}{x^2}+\frac{3}{x^4}-\frac{4}{x^6}+\ldots$
$=\frac{x^4}{\left(x^2+1\right)^2}$
Asked in: AP EAMCET 2006
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