- #1

lainyg

- 3

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## Homework Statement

q(n) = Sum(from k=1 to n) 1/n!

Exercise 3: Prove that {q(n)}n(forall)Ns is a cauchy sequence.

## Homework Equations

none.

## The Attempt at a Solution

So many attempts at a solution. I know that a sequence is a cauchy sequence if for all epsilons greater than 0 there exists an N such that m,n >N and therefore the absolute value of q(m) minus (qn) is less than epsilon. A sequence is considered a cauchy sequence of its terms approach a limit (and converge). My problem is with proving this as it is a sum, and not letting it get messy with double factorials. How do I prove this?