Please help me with this proof that follows:

Let x-sub-j from j=1 to infinity and y-sub-j from j=1 to infinity be sequences in the Integers such that x-sub-j <= y-sub-j for all j in the Natural numbers. Then for all k in the Naturals, prove that:

Σ from j=1 to k of (x-sub-j) <= Σ from j=1 to k of (y-sub-j)

Can we use induction here? Or recursion? Thanks a lot in advance!