Chapter 8: Infinite Sequences and Series

Section 8.2: Series

Example 8.2.6

$$ Test the series $\sum _{n\=1}^{\infty }\arctan \left(n\right)$ for convergence. $$ Solution $$ Determine the limiting behavior of $a_n\=\arctan \left(n\right)$  •  Calculus palette: Limit template≻Apply to $\arctan \left(n\right)$ •  Context Panel: Evaluate and Display Inline $\underset{n\to \infty }{lim}\arctan \left(n\right)$ = $\frac{1}{2}\mathrm{\π}$$$ $$ Because $a_n\=\arctan \left(n\right)\to \mathrm{\π}\/2$ and not 0 as $n\to \infty$, the series cannot converge. Hence it must diverge.

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