(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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

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

2. Relevant equations

none.

3. 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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Cauchy Sequence Problem

**Physics Forums | Science Articles, Homework Help, Discussion**