In the expansion of $(1+x{)}^7$, the sum of the coefficients of terms with even powers of $x$ is?

Step-by-step solution

1. Sum of all coefficients: $(1+1{)}^7=128$.
2. Sum of coefficients of even powers: $\frac{(1+1{)}^7+(1-1{)}^7}{2}$.
3. Compute $(1-1{)}^7=0$.
4. Thus sum = $(128+0)/2=64$.

Concept tested: Sum of even‑power coefficients in binomial expansion

Published 7 October 2026 · How this solution was prepared and checked