find the sum

Question

find the sum

anonymous · Answer

$$\sum_{n=1}^{\infty}\frac{ n+5 }{ 4n-6 }$$

anonymous · Answer

It's either going to converge or diverge.  From looking at it, I can see it diverging.  Which means it goes off to infinity

anonymous · Answer

does it diverge because the numerator and denominator have the same power?

solomonzelman · Answer

well, as n approaches infinity i the terms approach 1/4.

solomonzelman · Answer

so should converge

anonymous · Answer

Sometimes you can't tell, but ^

solomonzelman · Answer

the i in my reply shouldn't be there

anonymous · Answer

WolframAlpha says otherwise though

solomonzelman · Answer

surprising:)

anonymous · Answer

anonymous · Answer

The demoniator grows faster, so I would think the same

solomonzelman · Answer

oh, no... it is my mistake, because the terms are just approaching 1/4, but the sum is constantly growing each time by about 1/4 so it does diverge

anonymous · Answer

lol. so this is divergent then?

solomonzelman · Answer

well, sum grows by about 1.4, but you get the point

solomonzelman · Answer

:) -:(

anonymous · Answer

So there is either no sum, or the sum is infinity

solomonzelman · Answer

divergent = our friend
convergent = work work work

anonymous · Answer

just entered diverge, and DNE for sum and said it was correct

solomonzelman · Answer

"diverges " is the ans

solomonzelman · Answer

I like when it diverges actually. That means you can just say "diverges. Where as if it converges you have to show where converges and how.

anonymous · Answer

i meant diverges, sorry

solomonzelman · Answer

yhes diverges