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Question from Betsy, a student:
Use the ratio test to determine if the series is convergent or divergent.
1+1/2^2+1/3^3+1/4^4
I know the general terms are a(n)=1/n^n and a(n+1)=1/(n+1)^(n+1) but I can't simplify r=lim(n->inf.)=n^n/(n+1)^(n+1)

Betsy,

Don't simplify it, estimate it by something that is a little larger but still goes to zero (or a little smaller but still doesn't go to zero) and that you can simplify.

Good Hunting!
RD

 

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