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The coefficient of xn in expansion of (1+x)(1−x)n is
- a)(−1)n(n+1)
- b)(−1)n(1−n)
- c)(−1)n
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The coefficient ofxnin expansion of(1+x)(1−x)nisa)(−1)n(n+...
We can expand (1+x)(1−x)n as
= (1+x)(nC0− nC1.x + nC2.x2 + ........ +(−1)n nCnxn)
= (1+x)(nC0− nC1.x + nC2.x2 + ........ +(−1)n nCnxn)
Coefficient of xn is
(−1)n nCn + (−1)n−1 nCn−1
=(−1)n(1−n)
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