For the series sum(n=1)(inf) (-1)^n*a_n where a_n = 1/n when n is even

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SUMMARY

The series sum(n=1)(inf) (-1)^n*a_n, where a_n = 1/n for even n and a_n = 1/n^2 for odd n, exhibits divergent behavior due to the divergence of the even terms. Specifically, the even-indexed terms, which follow the harmonic series, diverge, while the odd-indexed terms converge to a finite value. Therefore, the overall series is classified as divergent.

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For the series sum(n=1)(inf) (-1)^n*a_n where a_n = 1/n when n is even and 1/n^2 when n is odd, is it divergent?
 
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welcome to pf!

hi ussscou! welcome to pf! :wink:

tell us what you think (and why), and then we'll comment! :smile:
 


ussscou said:
For the series sum(n=1)(inf) (-1)^n*a_n where a_n = 1/n when n is even and 1/n^2 when n is odd, is it divergent?

The even terms sum diverges, while the odd terms sum converges. Conclusion?
 

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