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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–1}C_{n}.

#### Options

True

False

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#### 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

= n^{th} terms and (n + 1)^{th} terms

Coefficient of nth term = ^{2n–1}C_{n–1}

And he coefficient of (n + 1)^{th} term = ^{2n–1}C_{n}

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`

= ^{2n}C_{n}

Concept: General and Middle Terms

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