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Prove that if k=1akconverges to L and k=1bkconverges to M , then the seriesk=1ak+bk=L+M.

Short Answer

Expert verified

k=1ak+bk=k=1ak+k=1bk=L+M.Hence,proved.

Step by step solution

01

Step 1. Given Information.

k=1ak=Landk=1bk=M.

02

Step 2. Proof.

We know that the sum of two convergent series is a convergent series itself.

k=1ak=L,andk=1bk=M.So,k=1ak+bk=k=1ak+k=1bk=L+M.Hence,proved.

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