A) \[\frac{1.3.5....(5n-1)}{n!}{{x}^{n}}\]
B) \[\frac{2.4.6....2n}{n!}{{x}^{2n+1}}\]
C) \[\frac{1.3.5....(2n-1)}{n!}{{x}^{n}}\]
D) \[\frac{1.3.5....(2n-1)}{n!}{{2}^{n}}{{x}^{n}}\]
Correct Answer: D
Solution :
Middle term of \[{{(1+x)}^{2n}}\]is \[{{T}_{n+1}}={{\,}^{2n}}{{C}_{n}}{{x}^{n}}\] \[=\frac{(2n)!}{n!\,\,n!}{{x}^{n}}=\frac{1.3.5....(2n-1)}{n!}{{2}^{n}}{{x}^{n}}\].
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