# The sum of coefficients of the two middle terms in the expansion of (1 + x)2n–1 is equal to 2n–1Cn. - Mathematics

MCQ
True or False

The sum of coefficients of the two middle terms in the expansion of (1 + x)2n–1 is equal to 2n–1Cn

• True

• False

#### Solution

This statement is False.

Explanation:

The given expression is (1 + x)2n–1

Number of terms = 2n – 1 + 1 = 2n  ....(Even)

∴ Middle terms are (2"n")/2 th term and ((2"n")/2 + 1)^"th" terms

= nth terms and (n + 1)th terms

Coefficient of nth term = 2n–1Cn–1

And he coefficient of (n + 1)th term = 2n–1Cn

Sum of the coefficients = ""(2n + 1)C_(n - 1) + ""^(2n - 1)C_n

= ""^(2n - 1)C_(n - 1) + ""^(2n - 1)C_n

= ""^(2n - 1 + 1)C_n

= 2nCn

Concept: General and Middle Terms
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#### APPEARS IN

NCERT Mathematics Exemplar Class 11
Chapter 8 Binomial Theorem
Exercise | Q 37 | Page 146

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