Sum of two middle terms in the expansion of (1+x)2n−1 is

# Sum of two middle terms in the expansion of $\left(1+x{\right)}^{2n-1}$ is

1. A

2. B

3. C

4. D

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### Solution:

Two middle terms in the expansion of $\left(1+x{\right)}^{2n-1}$ are $\left(\frac{2n-1+1}{2}\right)$th and $\left(\frac{2n-1+1}{2}+1\right)$th terms, that is, nth and (n+1)th terms.

Coefficients of the middle terms in the expansion of

$\left(1+x{\right)}^{2n-1}$ are  and  and their $\mathrm{sum}{=}^{2n-1}{C}_{n-1}{+}^{2n-1}{C}_{n}{=}^{2n}{C}_{n}$

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