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!

Calculating a finite series

  1. Jul 23, 2012 #1

    I would love some help on calculating the following sum for [itex]\alpha, \beta \in \mathbb{N}[/itex] and [itex]n \in \mathbb{N} \backslash \{0\}[/itex]:


    Thanks in advance,
  2. jcsd
  3. Jul 23, 2012 #2
    What did you already try to solve this problem?
  4. Jul 23, 2012 #3
    ([itex] n \geq 2 [/itex], of course) I tried to find an inductive formula by setting [itex] n = 2, n = 3 [/itex] and [itex] n = 4 [/itex], but don't find anything interesting. Of course we already knew that the thing is symmetric, symbolically it is also [itex] \displaystyle\sum_{i=1}^{n-1}i^{\beta}(n-i)^{\alpha} [/itex], but that's about all I find when I try to find an inductive formula. I think now that this might be the easiest way to express the series.
    What I eventually need is the behavior for large [itex] n [/itex], but thats [itex] \sim (n-1)^{\beta} + (n-1)^{\alpha} [/itex]. I came across this when I wanted to calculate [itex] \displaystyle\int_{0}^{1}x^m \mathrm{d}x [/itex] for [itex] m \geq 1 [/itex] explicitally using the Riemann sum.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook