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

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

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

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