The sequence b(n)= npicos(npi) coverges or diverges?

[Simkate]

The sequence b(n)= npicos(npi) coverges or diverges? if it converges what is the limit?

My Work

When n is even cosnpi= o and b(n)=o (therefore when n is oven it converges)
but
when n is odd cosnpi=-1 and b(n)= - infinity( thereofre when n is even it diverges)

is this correct?

 

[╔(σ_σ)╝]

cos(npi) is never zero. I think you are thing about sin(npi).

cos(npi) simply osscillates between 1 and -1.