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

1. Oct 15, 2011

### bolzano

Hi i have to show that the series 1+2r+r2+2r3+r4+2r5+... converges for r=$\frac{2}{3}$ and diverges for r=$\frac{4}{3}$ using the nth root test.

The sequence $\sqrt[n]{a_{n}}$comes a bit complicated so i was wondering if I can remove the 1st term a1=1 and show that 2r+r2+2r3+r4+2r5+... converges, using the test of course.

Am i doing something wrong?

Thanks :)

2. Oct 15, 2011

### HallsofIvy

Yes you can remove any finite number of terms and not change whether the series converges or not.

3. Oct 15, 2011

### bolzano

So $(\sqrt[n]{a_{n}})$$=2r,r,\sqrt[3]{2}r,r$,$\sqrt[5]{2}r,...$ which converges to $r$ right? :)