- #1
tarheelborn
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Homework Statement
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.
Homework Equations
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!