10.3 Sigma Notation and Infinite Series

Notes

Sigma notation $\displaystyle \sum_{k=1}^{n} a_k$ means add the terms $a_1 + a_2 + \dots + a_n$.

• $\displaystyle \sum_{k=1}^{n} k = \frac{n(n + 1)}{2}$ and $\displaystyle \sum_{k=1}^{n} k^2 = \frac{n(n + 1)(2n + 1)}{6}$.
• An infinite geometric series converges only if $|r| < 1$, and then $\displaystyle S = \frac{a_1}{1 - r}$.
• Example: $\displaystyle 8 + 4 + 2 + 1 + \dots = \frac{8}{1 - 1/2} = 16$.