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

I Find the formula to express the infinite series...

  1. Jun 27, 2016 #1
    The problem is to find the general term ##a_n## (not the partial sum) of the infinite series with a starting point n=1

    $$a_n = \frac {8} {1^2 + 1} + \frac {1} {2^2 + 1} + \frac {8} {3^2 + 1} + \frac {1} {4^2 + 1} + \text {...}$$

    The denominator is easy, just ##n^2 + 1## but I can't think of any way to get the numerator to alternate between 8 and 1.
     
  2. jcsd
  3. Jun 27, 2016 #2

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    ##4.5 + 3.5(-1)^{n+1}##
     
  4. Jun 27, 2016 #3
    Never mind I figured it out $$a_n = \frac {9 - 7 \{ -1 \} ^n} {2 \{ 1 + n^2 \}}$$
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Find the formula to express the infinite series...
  1. Infinite series (Replies: 1)

  2. Infinite Series (Replies: 11)

  3. Infinite Series (Replies: 2)

  4. Series expression (Replies: 2)

Loading...