Writing a sum of powers of 2 in sigma notation

First, express each term as a power of 2: $2 = 2^1$, $4 = 2^2$, $8 = 2^3$, $16 = 2^4$, and $32 = 2^5$. This shows the terms are $2^i$ for $i = 1, 2, 3, 4, 5$.

Since the sum starts at $i=1$ and ends at $i=5$, we can write the entire sum compactly as $\sum_{i=1}^{5} 2^i.$ You can check this by expanding it back out: $2^1+2^2+2^3+2^4+2^5 = 2+4+8+16+32$, which matches the original sum.