Question

how can we solve this question to investigate whether it is converging or diverging? => an = cos(pie)(n)

Answer 1

I guess you mean \[a_n = \cos(\pi n)\] So why don't you write down this series explicitly? Then you can see whether it converges or not.

Answer 2

This sequence will oscillate between 1 and -1. By the definition of the limit of a sequence, it does not converge (convergence requires a single value). It therefore does not converge.

Answer 3

very good, no more thinking required by the original poster

Answer 4

I have actually thought about it again before reading the replies :) thank you.