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

A
$^{2 n - 1} C_{n - 1}$
B
$^{2 n - 1} C_{n}$
C
$^{2 n} C_{n}$
D
$^{2 n} C_{n + 1}$

Solution:

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

Coefficients of the middle terms in the expansion of

$(1 + x)^{2 n - 1}$ are $^{2 n - 1} C_{n - 1}$ and $^{2 n - 1} C_{n}$ and their $sum =^{2 n - 1} C_{n - 1} +^{2 n - 1} C_{n} =^{2 n} C_{n}$

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

Solution:

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