Math miscellaneousEasy
Question
The coefficient of xn in expansion of (1 + x)(1 - x)n is
Options
A.(n - 1)
B.(- 1)n(1 - n)
C.(- 1)n-1(n - 1)2
D.(- 1)n-1n
Solution
Coefficient of xn in (1 + x)(1 - x)n = (1 + x)(nC0 - nC1x + ...... + (-1)n - 1nCn-1xn-1 + (-1)n nCn xn)
= (-1)n nCn + (-1)n-1 nCn-1 = (-1)n(1 - n).
= (-1)n nCn + (-1)n-1 nCn-1 = (-1)n(1 - n).
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