Convergent/Divergent
posted by What's the Difference? .
determine whether the series 1 + 1/2^5 + 1/3^5 + 1/4^5 +...is convergent or divergent?
How do I tell the difference?

do the ratio test:
ratio (An+1)/An=
the series is SUM (1/n)^5 for n=1>inf
ratio [(1/n+1)/ (1/n)]^5=(n/(n+1))^5 which is less than 1, so the series converges. This means, if you add all the terms, the sum will be a finite q 
do the ratio test:
ratio (An+1)/An=
the series is SUM (1/n)^5 for n=1>inf
ratio [(1/n+1)/ (1/n)]^5=(n/(n+1))^5 which is less than 1, so the series converges. This means, if you add all the terms, the sum will be a finite quanity. If the ratio had been 1 or greater, the series would have been divergent.
http://abacus.bates.edu/acad/acad_support/msw/convergence_tests.pdf