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

For each n \in N, let s_n = 1 + 1/2 + ... + 1/n. By considering s_2n - s_n, prove that {s_n} is not Cauchy.

2. Relevant equations

3. The attempt at a solution

I know that s_2n - s_n = (1 + 1/2 + ... + 1/n + 1/(n+1) + ... + 1/2n) - (1 + 1/2 + ... + 1/n)

= (1/(n+1) + 1/(n+2) + ... + 1/2n

> 1/2n + 1/2n + ... + 1/2n

= n * 1/2n = 1/2

Let \epsilon > 0. Then I need to find N \in N such that m, n >= N. So if I let N = 1/2...

And that's where I lose it. These don't work like regular epsilon proofs!

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# Homework Help: Cauchy sequence proof

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