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  • The sum of coefficients of the two middle terms in the expansion of 1+x exponent of 2n-1 is equal to 2n – 1 Combination of n.

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

Answers (1)

The given statement is False.

Given: (1 + x)2n-1

Now, no. of terms = 2n – 1 + 1

                     = 2n (even)

Thus, the middle term = 2n/2th terms & (2n/2 + 1)th terms

                                          = nth terms & (n+1)th terms

Now, the coefficient of-

nth  term = 2n – 1Cn-1

& (n + 1)th term = 2n-1Cn

Now, sum of the coefficients = 2n – 1Cn-1 + 2n-1Cn

                                                      = 2n-1Cn-1 + 2n-1Cn

                                                      = 2nCn

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