Find the sum of the coefficients of terms containing odd powers of $x$ in the expansion of $(1+2x{)}^7$.

Step-by-step solution

1. The sum of all coefficients is $f(1)=(1+2{)}^7=3^7=2187$.
2. The sum of coefficients of even powers is $(f(1)+f(-1))/2$.
3. Compute $f(-1)=(1-2{)}^7=(-1{)}^7=-1$.
4. Sum_even = (2187 + (-1))/2 = 2186/2 = 1093.
5. Sum_odd = total - even = 2187 - 1093 = 1094.
6. Hence the required sum is $1094$.

Concept tested: Sum of coefficients of odd powers

Published 16 October 2026 · How this solution was prepared and checked