I had a bit of trouble in testing series like this for convergence(adsbygoogle = window.adsbygoogle || []).push({});

$$\sum_{ n=1 }^{ \infty } \frac { 1 }{ 2n+1 } $$

If by the comparison test, ##\frac{ 1 }{ 2n+1 } < \frac{ 1 }{ 2n }## for all of n>0,

and ##\lim_{ n \rightarrow \infty} \frac{ 1 }{ 2n }## =0, then the series should be convergent.

However, the correct answer in my book is divergent.

Why is that so?

Thanks for any help

PS. Could any one help me with the LaTeX code? I can't seem to get it right.

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# Series test for convergence or divergence

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