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Help with testing the convergence of a series

  1. Oct 15, 2011 #1
    Hi i have to show that the series 1+2r+r2+2r3+r4+2r5+... converges for r=[itex]\frac{2}{3}[/itex] and diverges for r=[itex]\frac{4}{3}[/itex] using the nth 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 a1=1 and show that 2r+r2+2r3+r4+2r5+... converges, using the test of course.

    Am i doing something wrong?

    Thanks :)
  2. jcsd
  3. Oct 15, 2011 #2


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    Science Advisor

    Yes you can remove any finite number of terms and not change whether the series converges or not.
  4. Oct 15, 2011 #3
    So [itex](\sqrt[n]{a_{n}})[/itex][itex]=2r,r,\sqrt[3]{2}r,r[/itex],[itex]\sqrt[5]{2}r,...[/itex] which converges to [itex]r[/itex] right? :)
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