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)(n−1)/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)(n−1)/2, when n is an odd integer (1+x)(1+x2)−1 =(1+x)[1−x2+x4−x6...∞] =[1−x2+x4−x6...∞]+x[1−x2+x4−x6...∞] =[1−x2+x4−x6...∞]+[x−x3+x5−x7...∞] Hence both A and D are the correct answers.