AP Calculus BC / Unit 10: Infinite Sequences and Series
10.7 Alternating Series Test for Convergence
Notes
$\displaystyle \sum(-1)^nb_n$ converges if $b_n$ is positive, decreasing, and $\displaystyle \lim b_n=0$.
Practice
$\displaystyle \sum\frac{(-1)^n}{n}$:
$\displaystyle \frac{1}{n}$ decreases to 0.
$\displaystyle \sum(-1)^n\frac{n}{n+1}$:
$b_n\to1$, not 0.
Which is NOT a condition of the alternating series test?
That's absolute convergence, a separate idea.
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