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Cauchy Sequence Analysis and Examples by Tom Davis is a document available to read on EtoBox.

The document analyzes several sequences to determine if they are Cauchy sequences or not. It is shown that: (1) The sequence {an} = {n+(−1)n/(n+3)} is a Cauchy sequence since |an - am| can be made arbitrarily small by choosing a large enough n0. (2) The sequence {an} = {n/(n+1)} is not a Cauchy sequence since |an - an+1| is always greater than 1. (3) The sequence {an} = {√n} is not a Cauchy sequence since |an - am| can be made equal to 1/2 no matter how large

Author

Tom Davis

Language

EN