Register to reply

For which values of p does this sum converge?

by Jacob_
Tags: converge, values
Share this thread:
Jacob_
#1
Mar4-12, 11:09 PM
P: 1
1. The problem statement, all variables and given/known data
For which p > 0 does the sum
[itex]\displaystyle\sum\limits_{k=10}^∞ \frac{1}{k^p(ln(ln(k)))^p}[/itex]
converge?


2. Relevant equations
1/k^p converges for p > 1.


3. The attempt at a solution
I'm not really sure where to start. I want to use a comparison test with the p-series, but ln(ln(k)) < 1 for k < e^e, so the equation isn't greater or less than 1/k^p for the entire sum interval.
Phys.Org News Partner Science news on Phys.org
World's largest solar boat on Greek prehistoric mission
Google searches hold key to future market crashes
Mineral magic? Common mineral capable of making and breaking bonds
sunjin09
#2
Mar5-12, 01:30 PM
P: 312
Quote Quote by Jacob_ View Post
1. The problem statement, all variables and given/known data
For which p > 0 does the sum
[itex]\displaystyle\sum\limits_{k=10}^∞ \frac{1}{k^p(ln(ln(k)))^p}[/itex]
converge?


2. Relevant equations
1/k^p converges for p > 1.


3. The attempt at a solution
I'm not really sure where to start. I want to use a comparison test with the p-series, but ln(ln(k)) < 1 for k < e^e, so the equation isn't greater or less than 1/k^p for the entire sum interval.
Convergence of the series is determined only by the asymptotic behavior of the terms in the sum, for any finite k, the term is finite, and therefore irrelevant


Register to reply

Related Discussions
For which values of x does this series converge? Calculus & Beyond Homework 3
For which values of a does this series converge? Calculus & Beyond Homework 3
For what values of p does this series converge? Calculus & Beyond Homework 3
For what values of p and q will the following converge? Calculus & Beyond Homework 0
For what values of p does the series converge? Calculus & Beyond Homework 3