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.
- $a _ { n } = \cos n$

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.
-$$a _ { n } = \cos n$$
A) L = 1, N = 394
B) L = 0, N = 237
C) L = 0, N = 394
D) diverges

Quizplus · Accepted Answer

The sequence $a_n = \cos n$ does not converge to a single value as $n$ approaches infinity because the cosine function oscillates between -1 and 1 for all integer values of $n$. Therefore, the series diverges and does not have a limit $L$.

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