Summation - Example

Expand $\sum_{k=3}^{7} (2k + 1)$.

Substitute $k = 3, 4, 5, 6, 7$ into the expression $2k + 1$: $(2 \times 3 + 1) + (2 \times 4 + 1) + (2 \times 5 + 1) + (2 \times 6 + 1) + (2 \times 7 + 1)$.

This equals $7 + 9 + 11 + 13 + 15 = 55$. Sigma notation is compact, but you can always expand it to see what you're adding.