Question

Test for divergence or convergence for the series: \[\sum_{1}^{\infty}\frac{ 5^{x}}{3^{x}+4^{x}}\]

Answer 1

i wanna say it converges based on a ratio test

Answer 2

That's what I thought, but my book says it diverges

Answer 3

hmm, well I have been known to be wrong a time or two :)

Answer 4

lets see what the wolf says

Answer 5

http://www.wolframalpha.com/input/?i=lim+%28x+to+inf%29+5%5Ex%2F%283%5Ex%2B4%5Ex%29

well, it says diverge as well

Answer 6

http://www.wolframalpha.com/input/?i=sum+5%5Ex%2F%283%5Ex%2B4%5Ex%29+from+1+to+inf

same thing

Answer 7

What test would I use to show that it diverges?

Answer 8

comparison

Answer 9

limit test is what the wolf says, I tried what I thought was a ratio test on paper

Answer 10

Thank guys

Answer 11

*thanks

Answer 12

good luck ;)