Write the coefficient of the middle term in the expansion of $(1 + x)^{2 n} .$

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Solution

$(1 + x)^{2 n}$

Here k = 2n, which is even number.

So, $(\frac{2 n}{2} + 1) (n + 1) t h$ term is the middle term.

Coefficient of (r+1)th term in the binomial expansion of $(1 + x)^{k}$ is $k_{C_{r}}$

Coefficient of (n+1)th term in the binomial expansion of $(1 + x)^{2} n$ is ${2 n}_{C_{n}}$

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Write the coefficient of the middle term in the expansion of (1+x)2n.

(1+x)2n Here k = 2n, which is even number. So, (2n2+1)(n+1)th term is the middle term. Coefficient of (r+1)th term in the binomial expansion of (1+x)k is kCr Coefficient of (n+1)th term in the binomial expansion of (1+x)2n is 2nCn

Write the coefficient of the middle term in the expansion of $(1 + x)^{2 n} .$

$(1 + x)^{2 n}$

Here k = 2n, which is even number.

So, $(\frac{2 n}{2} + 1) (n + 1) t h$ term is the middle term.

Coefficient of (r+1)th term in the binomial expansion of $(1 + x)^{k}$ is $k_{C_{r}}$

Coefficient of (n+1)th term in the binomial expansion of $(1 + x)^{2} n$ is ${2 n}_{C_{n}}$