One or more options can be correct.

Find the coefficient of $x^{100}$ in $(1 - x)^{- 3}$ .

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Solution

The correct option is C

From binomial expansion $(1 - x)^{- 3}$ can be written as $(1 +^{3} C_{1} x +^{4} C_{2} x^{2} + . . . . . . . . . . . . . . +^{100 + 2} C_{100} x^{100} + . . . . . . . . .)$

Coefficient of $x^{100}$ in = $^{100 + 2} C_{100}$ = $^{102} C_{2}$

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Similar questions

One or more options can be correct:
Find the coefficient of $x^{10}$ in $(1 - x^{7}) (1 - x^{8}) (1 - x^{9}) (1 - x)^{- 3}$

x^{100}

\frac{3 - 5 x}{(1 - x)^{2}}

x^{50}

(1 + x)^{100} + 2 x (1 + x)^{99} + 3 x^{2} (1 + x)^{98} + . . . . . . . . . + 101. x^{100}

10

1

4

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