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anonymous
 5 years ago
Does this infinte series converge or diverge? Sigma from 1infinity of 1n(n)/n^1.02
anonymous
 5 years ago
Does this infinte series converge or diverge? Sigma from 1infinity of 1n(n)/n^1.02

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\sum_{1}^{\infty} \ln(n)/n^1.02\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Use the integral test you will find it will converge.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Are you familiar with integral test? Or should I go on?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0In case you aren't If \[\int\limits_{k}^{\infty} f(x) dx \] is convergent implies \[\sum_{k}^{\infty}\an] is convergent

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\sum_{k}^{\infty}an\] is convergent

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0take \[f(x) = \frac{\ln(n)n^(1.02)}\] and k = 1

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0f(x) = ln(n)/n^(1.02) take the integral from 1 to inf and show it does not diverge that is it has a finite answer. That will mean our series also converges. =]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i am also interested in this problem, and i'd love to use the integral test, but i don't know how to integrate that. would you do it by parts?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0let u=ln(n), dv=n^(1.02)? see but from here what would v be?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0sorry, i don't mean to hijack the problem, it's just the same thing i've been having trouble with, too.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oh and i meant dv=n^(1.02)dx

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0unless i'm setting u and dv to the wrong parts

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0v is something stupid 50/n^(0.02)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0...what. where did the 50 come in?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i can see the power rule making the exponent come down to 0.02, and also kicking the negative out front, but 50? where did that come from?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.01.02 = 1 + 1/50, sorry I hate decimals

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oh right, i see. thanks.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oh i am so good with this now. but then i definitely stole this question from the original poster, so... sorry about that, Aubun.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Okay! I'm off to bed, have a big math test tomorrow
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