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Just by looking at it's easy for me to say that $\sum\limits_{n=1}^\infty \frac 3 {25n}$ converges. But how can I prove it?

If I try to do it by the fraction criteria ($\lim\limits_{n\to \infty} |\frac {a_n+1} {a_n}|<1)$ I actually end up with $1<1$ what's not supposed to be true. What am I misisng out on?

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    You can upper or lower bound that sum by an integral $\int \frac{3}{35t}dt$. – 2017-01-11
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    It doesn't converge!!! – 2017-01-11
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    It doesn't converge. – 2017-01-11
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    I guess that postulating convergence was a fatal error ;) – 2017-01-11

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Hint: $\sum\limits_{n=1}^\infty \frac 3 {25n}=\frac{3}{25}\sum\limits_{n=1}^\infty \frac{1}{n} $ and that is the Harmonic Series which diverges