Ok so you can't apply the quotient criteria to the harmonic series because:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]lim_{k\to \infty}|\dfrac{a_{k+1}}{a_k}|[/tex]

applied to the harmonic series:

[tex]lim_{k\to \infty}|\dfrac{1/(k+1)}{1/k}| = lim_{k\to \infty}|\dfrac{k}{k+1}| < 1[/tex]

which does fullfill the quotient criteria, yet the harmonic series diverges...

So where else does it not work?

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# Quotient criteria and the harmonic series

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