- #1
utleysthrow
- 25
- 0
Homework Statement
[tex]\sum^{\infty}_{n=1} \frac{n}{2^{n}}[/tex]
Does this series converge or diverge?
Homework Equations
The Attempt at a Solution
By the Cauchy condensation test (http://en.wikipedia.org/wiki/Cauchy_condensation_test) I think this one diverges. But not sure if I am using it correctly.
According to the test,
[tex]\sum^{\infty}_{n=1} \frac{n}{2^{n}}[/tex]
converges if and only if
[tex]\sum^{\infty}_{n=1} 2^{n} \frac{2^{n}}{2^{n}} = \sum^{\infty}_{n=1} 2^{n}[/tex]
converges, which doesn't.
Thank you for any help.