# result about arithmetic of convergent sequences

#### Magnitude

Hello all,

I believe that, given a collection of increasing sequences whose total sum converges, each individual sequence will also converge. Attached is my short proof. Is it correct?

Regards,

Magnitude

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#### v8archie

Math Team
Your first line seems to state that all the sequences diverge.

1. You need only prove the result for two sequences. The result for $n$ sequences follows by induction.