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Design
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Homework Statement
Prove that if two sequences an and bn 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 an -> L and bn -> M we want an + bn -> L+M.
So I have |an - L | < Ε for every n > N
and |bn - L | Ε every n > N
What is my next step?
thank you
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