- #1

Design

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## Homework Statement

Prove that if two sequences a

_{n}and b

^{n}converge to L and M respectively, then the sum of the sequences converge to L+M.

Present a counter example to show the sum of two divergent sequences need not be divergent.

## The Attempt at a Solution

We have a

_{n}-> L and b

_{n}-> M we want a

_{n}+ b

_{n}-> L+M.

So I have |a

_{n}- L | < Ε for every n > N

and |b

_{n}- L | Ε every n > N

What is my next step?

thank you

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