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

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SUMMARY

The sequence b(n) = n * cos(nπ) diverges for odd values of n and converges to 0 for even values of n. When n is even, cos(nπ) equals 1, resulting in b(n) = n, which diverges to infinity. Conversely, for odd n, cos(nπ) equals -1, leading to b(n) = -n, which also diverges to negative infinity. The oscillatory nature of cos(nπ) confirms that it does not equal zero, but rather alternates between 1 and -1.

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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?
 
Last edited:
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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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