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Question

The coefficient of xk in the expansion of
E=1+(1+x)+(1+x)2+....+(1+x)n is

A
nCk
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B
n+1Ck
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C
n+1Ck+1
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D
none of these
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Solution

The correct option is C n+1Ck+1
Given, E=1+(1+x)+(1+x)2+...(1+x)n
=1(1+x)n+11(1+x)
=1x[(1+x)n+11]
Hence, xk =xk+1x
Coefficient of xk will be
n+1Ck+1

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