Use the root test for these
This might seem super easy, but could anyone give me some hint how to show the following An is convergent?
1.n!/n^n
2.(1-1/n)^(n^2)
3. 1-cos (1/n)
I've tried the limit test/ratio test, but not working. Maybe comparison test?
Also, could anyone help calculating the series using taylor expansion of cos?
the sum of all (cos n)/(2^n) where n goes from 0 to infinity?
Any help is greatly appreciated!