14.Find the coefficients of x in (1+x)n(1-x)n and hence show that : que marked in pic.

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The coefficient of $\frac{1}{x}$ in the expansion of $(1 + x)^{n} {(1 + \frac{1}{x})}^{n}$ is

Q. If n is a positive integer, find the coefficient of

x^{- 1}

in the expansion of

(1 + x)^{n} (1 + \frac{1}{x})^{n}

Q. Coefficient of

\frac{1}{x}

in the expansion of

(1 + x^{n}) {(1 + \frac{1}{x})}^{n}

Q. If

{(1 + x)}^{n} = n \sum r = 0 C_{r} x^{r}

, then the coefficient

x^{4}

in the product of

{(1 + x)}^{n} {(1 - x)}^{n}

Find the coefficient of $x^{4}$ in the expansion of $(1 + x)^{n} (1 - x)^{n}$ . Deduce that $C_{2} = C_{0} C_{4} - C_{1} C_{3} + C_{2} C_{2} - C_{3} C_{1} + C_{4} C_{0},$ where, $C$ stands for $^{n} C_{r} .$

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