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.
- $a _ { n } = ( 1 + 0.153 / n ) ^ { n }$

Question

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.
-$$a _ { n } = ( 1 + 0.153 / n ) ^ { n }$$
A) $\mathrm { L } \approx 1.1653 , \mathrm {~N} = 6$
B) $\mathrm { L } \approx 1.153 , \mathrm {~N} = 6$
C) $\mathrm { L } \approx 1.1653 , \mathrm {~N} = 2$
D) diverges

Quizplus · Accepted Answer

The Answer of 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.
-$$a _ { n } = ( 1 + 0.153 / n ) ^ { n }$$
A) $\mathrm { L } \approx 1.1653 , \mathrm {~N} = 6$
B) $\mathrm { L } \approx 1.153 , \mathrm {~N} = 6$
C) $\mathrm { L } \approx 1.1653 , \mathrm {~N} = 2$
D) diverges

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