Use what test?
a) ∑(from n=1 to infinity) (arctan n/ n^1.2)
b) ∑(from n=1 to infinity) ( (n^n) / (2n)! )
Not sure how to do these...when i do it using ratio test, it turns out really weird..so yea i need help.
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.
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.