By Calculating an Appropriate Number of Terms, Determine If the Series

question 406

Multiple Choice

By calculating an appropriate number of terms, determine if the series converges or diverges. If it converges, find the limit $L$ and the smallest integer $N$ such that $\left| a _ { n } - L \right| < 0.01$ for $n \geq N$ ; otherwise indicate divergence.
- $$a _ { n } = \frac { \tan ^ { - 1 } n } { e ^ { n } }$$

• A) \(\mathrm { L } = \frac { \pi } { \mathrm { e } } , \mathrm { N } = 8\)
• B) \(\mathrm { L } = \frac { \pi } { 2 \mathrm { e } } , \mathrm { N } = 6\)
• C) \(L = 0 , N = 5\)
• D) diverges

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