Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Help me with this series please:

  1. Nov 5, 2007 #1
    So, I have the series from 1 to infinity of

    sqrt(n)/(1+n^6)

    Now, we are supposed to show that the ratio test is inconclusive for this series. But when I apply the ratio test, I get:

    (n+1)^(1/2)/((1+(n+1)^6)*the original series and nothing seems to be cancelling out.

    Can anyone tell me if I am doing this properly?

    Thank you.
     
  2. jcsd
  3. Nov 5, 2007 #2

    dynamicsolo

    User Avatar
    Homework Helper

    OK, first of all, you should be dividing (n+1)^(1/2)/((1+(n+1)^6) by the original term, [n^1/2]/[1+(n^6)]. Secondly, nothing will generally cancel: you are supposed to take the limit of the absolute value of this ratio as n approaches infinity. Group the "like factors" together to form ratios like [1+(n^6)]/[1+({n+1}^6)] and look at the infinite limit of those ratios. You will find that the limit of the product of these ratios you've formed gives you 1 (i.e., the Ratio Test is useless here).
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook