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Question

The coefficient of xn,nϵN, in the expansion of 1+x1+x2 is

A
(1)n/2, when n is an even integer
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B
0, when n is an odd integer
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C
1, when n is an even integer
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D
(1)(n1)/2, when n is an odd integer
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Solution

The correct options are
A (1)n/2, when n is an even integer
B (1)(n1)/2, when n is an odd integer
(1+x)(1+x2)1
=(1+x)[1x2+x4x6...]
=[1x2+x4x6...]+x[1x2+x4x6...]
=[1x2+x4x6...]+[xx3+x5x7...]
Hence both A and D are the correct answers.

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