1. I believe it's zero because e-e=0....
There's a segment of the series that equals e.
I don't know about 2. though.
I'm prette sure the first sum diverges. One can check that
for integer .
Now, the harmonic series
diverges, and so
diverges as well.
but since for
then
and so by the comparison test, both sums diverge, and since
,
your series in problem 1 diverges.
--Kevin C.