1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

How this summation is to 3?

  1. Oct 8, 2009 #1
    Hi everyone.
    I hardly remember the fomulas of summation of sequence.

    I got this problem.


    The result is 2.5.
    How can I solve this problem?

    Thanks all. :)
    Last edited: Oct 9, 2009
  2. jcsd
  3. Oct 8, 2009 #2
    Assuming |r| < 1 then

    [tex]\sum_{n=0}^{\infty} r^n = \frac{1}{1-r}[/tex]

    Differentiation both sides with respect to r gives:

    [tex]\sum_{n=1}^{\infty} n \cdot r^{n-1} = \frac{1}{(1-r)^2}[/tex]

    This should give you a push in the right direction.

    (Warning: Be careful of your initial index.)

  4. Oct 9, 2009 #3
    You suggested me very good approach.
    However, the problem still remains,,,

    my equation is n vs (n-2), not n vs (n-1)

  5. Oct 9, 2009 #4


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Raising it to the power of n-2 instead of n-1 is just dividing it by 3/4. You should be able to find a way to modify your series so that you have an n-1 in the exponent
  6. Oct 9, 2009 #5
    You are absolutely right.
    I was so stupid.

    Thank you ;-)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook