Hi i have to show that the series 1+2r+r(adsbygoogle = window.adsbygoogle || []).push({}); ^{2}+2r^{3}+r^{4}+2r^{5}+... converges for r=[itex]\frac{2}{3}[/itex] and diverges for r=[itex]\frac{4}{3}[/itex] using the n^{th}root test.

The sequence [itex]\sqrt[n]{a_{n}}[/itex]comes a bit complicated so i was wondering if I can remove the 1st term a_{1}=1 and show that 2r+r^{2}+2r^{3}+r^{4}+2r^{5}+... converges, using the test of course.

Am i doing something wrong?

Thanks :)

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# Homework Help: Help with testing the convergence of a series

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