Q. 12

# Find the sum of coefficients of two middle terms in the binomial expansion of (1 + x)^{2n-1}

Answer :

Given:

Total terms after expansion = 2n-1+1=2n

Middle term = 2n/2 = nth term

So two required middle terms are : nth & (n+1)th term

k= (n-1) & n for both terms respectively.

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

Coefficient of nth term;

=^{2n-1}C_{n-1}

Coefficient of (n+1)th term ;

= ^{2n-1}C_{n}

Sum of coefficients = ^{2n-1}C_{n-1} + ^{2n-1}C_{n}

= ^{2n-1+1}C_{n}

=^{2n}C_{n}

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