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Question

(1+x)nnx1 is divisible by (where n ϵN)

A
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B
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C
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D
All of these
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Solution

The correct option is B
(1+x)n=1+nx+n(n1)2!x2+n(n2)3!x3+
(1+x)nnx1
=x2[n(n1)2!+n(n1)(n2)3!x+]
From above it is clear that (1+x)nnx1 is divisible by x2
Trick : (1+x)nnx1. Put n=2 and x=3; Then 422.31=9 is not divisible by 6, 54 but divisible by 9.
Which is given by option (b) i.e., x2=9

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