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!

Homework Help: Infinite sum of infinite negative series e^(-nt)

  1. Apr 15, 2012 #1
    Find the sum of
    e^(-nt) as n = 0,1,2,3,...

    Apparently it's 1/(1-e^-t)

    Can't use normal geometric series formula though as if a =1, r = e?
    Any ideas
    Thanks :)
     
  2. jcsd
  3. Apr 15, 2012 #2

    Curious3141

    User Avatar
    Homework Helper

    As long as t>0, you can treat this as the sum of an infinite geometric series.

    The common ratio is e^(-t), which has magnitude less than 1. First term is e^0 = 1.

    The sum is a/(1-r) = 1/(1-e^(-t)).
     
  4. Apr 15, 2012 #3
    of course when the condition of a=1 occurs it's just 1/(1-r). it was very easy then. doh :)
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook