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Can someone please help me prove that

the lim as n goes to infinity of (the sequence an + the sequence bn) = (the lim of an) + (the lim of bn).

What I think is that if one adds the two limits an + bn, she will come up with a new sequence cn and take its limit, which equals L. Then if she takes the limit of an and set it equal to L1 and take the limit of bn and set it equal to L2...

After this I don't know. I don't even know if this makes sense. Someone please help me!

I hope all of this makes sense. :)

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# Math Beauty and Her Limits

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