Comparison test:
let
, and let
Then
(because
)
And
is a p-series with p=1.2, which is greater than 1, therefore
converges, and because
is monotonic and increasing, and bounded above by
we know that
converges by the comparison test.
Ratio Test:
, and
Here multiply numerator and denominator by 1 over n^n to get
Now multiply the numerator and denominator by 1/n to get
It should be relatively clear that this converges to zero, (because the numerator converges to e, and the denominator diverges) but if you need me to explain that more, I can.
So because
the series
is absolutely convergent and therefore convergent.