First slide

Binomial theorem for positive integral Index

Question

The sum of the coefficients of even powers of x in the expansion of ${({1+x+x}^{2} {+x}^{3})}^{5} is$

Easy

A

510
B

512
C

521
D

522

Solution

$\begin{aligned} Sum of the coefficients of odd powers of x in f (x) is \\ \frac{f (1) - f (- 1)}{2} = \frac{(1 + 1 + 1)^{5} - (1 + 1 + 1)^{5}}{2} = \frac{4^{5}}{2} = 512 \end{aligned}$

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