I have to answer the following true or false questions. But also be able to explain why. I think I have the first 2 right saying they are both true. But I can't really explain why and I don't know about the last 2.

True or False

a) If a series does not converge, then its nth term does not approach 0 as n approaches infinity.

b) If the nth term of a series does not approach 0 as n approaches infinity, then the series diverges.

c) If all partial sums of a series are less than some constant L, then the series converges.

d) If a series converges, then there is a constant L such that all of its partial sums are less than L.