I think it is indeed possible, but probably so difficult in cases like these it is
impractical to do. That is why easy ones are always given as examples when illustrating the technique.
Using the right endpoint method:
. Which is what you have as well.
Just for fun, I ran this through Maple to see what it would give.
This sum equals....check this out:
Now, taking the limit, it is 1...as hoped/expected.
I wasn't about to attempt this by hand.
Now, for the even more difficult
Whose sum is
I am not about to type out what Maple gave back for this. But taking the limit gives:
My point being, yes it is possible, but it is so laborious to be impractical.
Give it a go if you have that much free time.