Using the integral test, how do you show whether #sum (1/n^2)cos(1/n) # diverges or converges from n=1 to infinity?
2 Answers
The
Explanation:
Note that
So by the integral test
Now
Therefore:
is a sum of non-negative terms, bounded above and therefore convergent.
Hence:
is convergent.
If you insist on using the integral test, you need to find
.
Use substitution with
The integral converges, so the series also converges.
(I think it is obvious that the function