How would one prove that the sum of 2 cauchy sequences is cauchy? I said let e>0 and take 2 arbitrary cauchy sequences then(adsbygoogle = window.adsbygoogle || []).push({});

|Sn - St|<e/2 whenever n,t>N1 and |St - Sm|<e/2 whenever t,m >N2.

So

|Sn - Sm|=|Sn - St + St - Sm|<= |Sn - St|+|St - Sm|< e/2 + e/2 <= e

So n,m>max{N1, N2} imples |Sn - Sm|<e thus cauchy

Am I close or way off?

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# Homework Help: Easy cauchy sequence prob

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