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Question: Answered & Verified by Expert
The greatest coefficient in the expansion of $(1+x)^{2 n+2}$ is
MathematicsBinomial TheoremJEE Main
Options:
  • A $\frac{(2 n)!}{(n!)^2}$
  • B $\frac{(2 n+2)!}{\{(n+1)!\}^2}$
  • C $\frac{(2 n+2)!}{n!(n+1)!}$
  • D $\frac{(2 n)!}{n!(n+1)!}$
Solution:
1979 Upvotes Verified Answer
The correct answer is: $\frac{(2 n+2)!}{\{(n+1)!\}^2}$
Greatest coefficient of $(1+x)^{2 n+2}$ is $={ }^{(2 n+2)} C_{n+1}=\frac{(2 n+2)!}{\{(n+1)!\}^2}$

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