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

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- Jul 27th 2011, 07:33 PMdbuchanan2730Real Analysis Proof
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 - Jul 27th 2011, 09:08 PMJG89Re: Real Analysis Proof
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.