# Convergent/Divergent

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determine whether the series 1 + 1/2^5 + 1/3^5 + 1/4^5 +...is convergent or divergent?

How do I tell the difference?

• Convergent/Divergent -

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

• Convergent/Divergent -

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.

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