Summation: Compute the exact sums

This one's a discrete mathematics question strictly due to its notation.

Compute the exact sums of the following: **(SHOW YOUR WORK)**

a) where is an integer between 1 and (I have no idea how to answer this one)

b) (I believe I have the answer, but I lack the steps and process to reach the answer)

c) (I may have answered this one, but I'd like confirmation)

d) (This one was easy, and I've already answered it)

This shouldn't be too hard for some people, but I'd rather not get these wrong.