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Combination

If n > 1, t...

Question

If $n > 1$ , then $(1 + x)^{n} - n x - 1$ is divisible by:

x^{5}

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x^{2}

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x^{3}

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x^{4}

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Solution

The correct option is B $x^{2}$
$(1 + x)^{n} = 1 +^{n} C_{1} x +^{n} C_{2} x^{2} + . . . . . . . +^{n} C_{n} x^{n}$
$(1 + x)^{n} - n x - 1$
$= (1 +^{n} C_{1} x + . . . . . . . . +^{n} C_{n} x^{n}) - n x - 1$
$=^{n} C_{2} x^{2} + . . . . . . +^{n} C_{n} x^{n}$
This is divisible by $x^{2}$

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