I was having a problem with a hw question. Could some give me a detailed proof to answer.
Prove that if the series ak converges and the series bk diverges then series ak+bk diverges.
I know i need to prove by contradiction. thanks
Suppose c_k = (a_k + b_k) converges. Then by our limit laws c_k - a_k must converge as well. But c_k - a_k = (a_k + b_k) - a_k = b_k, and we know that b_k diverges. This is the contradiction we're looking for.