## anonymous 5 years ago how can we solve this question to investigate whether it is converging or diverging? => an = cos(pie)(n)

1. nowhereman

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.

2. anonymous

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.

3. nowhereman

very good, no more thinking required by the original poster

4. anonymous

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