First slide

Binomial theorem for positive integral Index

Question

$In the expansion of (1 + x)^{30}, the sum of the coefficients of odd powers of x is$

Moderate

A

$2^{30}$
B

$2^{31}$
C

0
D

$2^{29}$

Solution

$We have, (1 + x)^{30} = 1 + {}^{30}C_{1} x + {}^{30}C_{2} x^{2} + {}^{30}C_{3} x^{3} + \dots + {}^{30}C_{29} x^{29} + {}^{30}C_{30} x^{30} Therefore, sum of coefficient of odd powers of x is {}^{30}C_{1} + {}^{30}C_{3} + \dots . + {}^{30}C_{29} = 2^{30 - 1} = 2^{29}$

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