AP Calculus BC / Unit 10: Infinite Sequences and Series
10.2 Working with Geometric Series
Notes
$$\sum_{n=0}^\infty ar^n=\frac{a}{1-r}\quad\text{if }|r|<1$$
- If $|r|\ge1$, it diverges.
Practice
$\displaystyle \sum_{n=0}^\infty\left(\frac{1}{3}\right)^n=$
$\displaystyle \frac{1}{1-1/3}$.
$\displaystyle \sum_{n=1}^\infty 4\left(\frac{1}{2}\right)^n=$
First term 2: $\displaystyle \frac{2}{1-1/2}$.
$\displaystyle \sum_{n=0}^\infty\left(-\frac{5}{4}\right)^n$:
$|r|>1$.
Ready for more? Take the Unit 10 test.