The coefficient of $x^{n}$ in the binomial expansion of ${(1 - x)}^{- 2}$ is

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Solution

${(1 - x)}^{- 2} = 1 + 2 x + 3 x^{2} + . . . . . . . . . . . . . . + (n + 1) x^{n} + . . . . . .$
The coefficient of $x^{n} = n + 1$

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The coefficient of xn in the binomial expansion of 1-x-2 is

1-x-2=1+2x+3x2+..............+n+1xn+......The coefficient of xn=n+1

The coefficient of $x^{n}$ in the binomial expansion of ${(1 - x)}^{- 2}$ is

${(1 - x)}^{- 2} = 1 + 2 x + 3 x^{2} + . . . . . . . . . . . . . . + (n + 1) x^{n} + . . . . . .$
The coefficient of $x^{n} = n + 1$