1
$\begingroup$

$$\sum_{n=1}^\infty \frac{5+2^n}{6+2^n} $$

I have this problem, and I am really lost on how to go about it, I was considering using a geometric series test however, even when I split the fraction, I couldn't see how to get the correct form for a geometric series. I am also not sure of how using any other tests such as the limit comparison, integral, ratio or root test would work.

Any push in the right direction would be helpful.

Thank you!

  • 4
    The general terms tends to $1$: the series is divergent. – 2017-01-07

1 Answers 1

0

It fails the term test, since

$$\lim_{n\to\infty}\frac{5+2^n}{6+2^n}=1$$

So the terms never approach $0$.

  • 0
    If I did the term test in any other case, and instead of 1 i got a 0, could I conclude that it converges? Or does it not work that way – 2017-01-07
  • 0
    @aa21 It does not work the other way around. Consider the classic harmonic series for example. – 2017-01-07
  • 0
    @aa21 No problem :-) – 2017-01-08