## For which positive real numbers a does the series converge

so it converges when r>1?
 if r>1 which would make -p=r, what values for a would make log(a) negative?

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 Quote by .d9n. does it converge if p<-1
That sounds good. So you want log(a)<(-1), right? Solve that for a. What's the inverse function to a log? And I don't think they mean log to the base 10.
 so -1

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 Quote by .d9n. so -1
No again to the first line. But yes to the second. e^(log(a))=a. Take log(a)<(-1) and exponentiate both sides of the inequality.
 so a

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 Quote by .d9n. so a
Now you've got it. And you also need 0<a. Otherwise the log (or your original series) isn't even defined.
 so sum n=1 to infinity of a^log(n) converges when 0

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