This is the series:
So this is what I did:
So the first term diverges because it is harmonic and thus the hole series diverges.
I have this marked as wrong, but I don't understand why. Can somebody explain it please?
Ok so I got this series:
Which converges as the limit comparison with 1/n^2 confirms.
But now I'm asked to express the result of the sum.
I think this is a telescoping series, isn't it?
If it is, then the sum is equal to the limit when N goes to infinity of the first term minus the N-th term?
Be very careful !
The sum of a divergent series and a convergent series is indeed divergent.
But the sum of 2 divergent series is not necessarily divergent.
Another way of doing it :
We can transform the second one by changing the indice :
So the sum is now :