[tex](adsbygoogle = window.adsbygoogle || []).push({});

\sum\limits_{n = 1}^\infty {\frac{{\sin \left( {\frac{{n\pi }}{2}} \right)}}{{11 + 8n}}}

[/tex]

I know that the numerator oscillates between -1 and 1 but there are some values of n for which the sine term also takes on the value of zero. So I can't find an explicit form for the numerator which means I can't use the alternating series test. I can't think of any other tests to use since the expression inside the summation takes on negative values 'regularly.'

[tex]

\sum\limits_{n = 1}^\infty {\left( { - 1} \right)^n \frac{1}{{n^{1 + \frac{1}{n}} }}}

[/tex]

Hmm...this one is a bit trick so basically I just hoped that the alternating series test would yield something simple.

[tex]

n^{1 + \frac{1}{n}} \ge n^{1 + \frac{1}{{n + 1}}} \Leftrightarrow \frac{1}{{n^{1 + \frac{1}{n}} }} \le \frac{1}{{n^{1 + \frac{1}{{n + 1}}} }}

[/tex]

[tex]

a_n \le a_{n + 1}

[/tex]

The terms are not decreasing so the series diverges? My caculator suggests otherwise. Again, I'm not sure about this one.

Can someone help me out with these two series?

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# Homework Help: Convergence/divergence of series

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