Calculate coefficient of $x^{10}$ in the $(1 + x)^{- 1}$

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Solution

$(1 + x)^{n} = 1 + n x + \frac{n (n - 1)}{2!} x^{2} + \frac{n (n - 1) (n - 2)}{3!} x^{3} + . . . .$
Here put $n = 1$
$(1 + x)^{- 1} = 1 - x + x^{2} - x^{3} + x^{4} - x^{5} . . . . .$
we need coefficient of $x^{10}$
$∴$ Coefficient of $x^{10}$ is $+ 1$

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