AP Calculus BC / Unit 10: Infinite Sequences and Series
10.3 The nth Term Test for Divergence
Notes
If $\displaystyle \lim_{n\to\infty}a_n\ne0$, then $\displaystyle \sum a_n$ diverges.
Practice
$\displaystyle \sum\frac{n}{n+1}$:
The terms approach 1, not 0.
$\displaystyle \lim a_n=0$. Then $\displaystyle \sum a_n$:
The test doesn't apply.
Which diverges by the nth term test?
$\cos(1/n)\to1$.
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