I have this question about proving that the sequence have non real limit
$$
U_n=1+\dfrac{1}{2}+...+\dfrac{1}{n}
$$
I've proved that $1<U_n<n$
is that enough ?or it's wrong
Thanks for helping
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The inequality $1<U_n<n$ for any $n\geq 2$ is correct, but it does not allow to conclude anything about the convergence or divergence of $U_n$. Something like $U_n\geq \log(n)$, on the other hand... – Jack D'Aurizio Apr 23 '17 at 18:10
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Can I ask about another thing I saw that prove by $U_{2^n}$ but I didn't mange to know how to write in that form can u just clarify this point – AbdulQader Qassab Apr 23 '17 at 18:30
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have a look at https://en.wikipedia.org/wiki/Cauchy_condensation_test – Jack D'Aurizio Apr 23 '17 at 18:31