Could some one please provide me with a detailed proof of the following linear properties of Expectation. I found a couple of informal proofs for these on the internet which dont outline the fact that how are the constants taken out of the Event of the probability and the infinite summation.

Property 1: E(X+c)=E(X)+E(c)

Property 2: E(aX) = aE(X)$

where E(X) = \sum_n n Pr(X=n)

Thanks.