Some help with this sequence proof would be appreciated!

Let x-sub-j from j=1 to infinity and y-sub-j from j=1 to infinity be sequences in the Integers, and let a,b,c in the Integers be such that a <= b < c

Prove that:

Σ from j=a to b of (x-sub-j + y-sub-j) = Σ from j=a to b of (x-sub-j) + Σ from j=a to b of (y-sub-j)

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