Find the smallest value of N that will make the inequality hold for all n N.
-$$a _ { n } = \cos n$$
A) $\mathrm { L } = 1 , \mathrm {~N} = 394$
B) $\mathrm { L } = 0 , \mathrm {~N} = 237$
C) $\mathrm { L } = 0 , \mathrm {~N} = 394$
D) diverges

Question

Find the smallest value of N that will make the inequality hold for all n > N.
-$$a _ { n } = \cos n$$
A) $\mathrm { L } = 1 , \mathrm {~N} = 394$
B) $\mathrm { L } = 0 , \mathrm {~N} = 237$
C) $\mathrm { L } = 0 , \mathrm {~N} = 394$
D) diverges

Quizplus · Accepted Answer

The sequence $a_n = \cos n$ does not converge to a single value as $n$ increases because the cosine function oscillates between -1 and 1 for all integer values of $n$. Therefore, there is no smallest value of $N$ that will make the inequality hold for all $n > N$, indicating that the sequence diverges.

Find the Smallest Value of N That Will Make the Inequality