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