TITLE: Convergence of $1 +\frac{1}{5}+\frac{1}{9} +\frac{1}{13}+\dots$
QUESTION [5 upvotes]: This is probably incredibly simple, but we've just started the topic, and we've just gone over geometric series, p-series, and harmonic series. Its simple when the series is given explicitly in sigma-notation, but I struggle when they don't give you the form and just give you the first few numbers. The question exactly is:
Determine whether the following series converges or diverges. Give a reason for your answer.
$$1+\frac15+\frac19+\frac1{13}\dots$$
Any tips/hints/help would be much appreciated.

REPLY [4 votes]: You could also observe that 
$$1 +\frac{1}{5}+\frac{1}{9}\cdots \geq 1 + \frac{1}{5}\left (1 +\frac{1}{2}+\frac{1}{3} +\cdots\right)$$
The term inside brackets is the harmonic series which....