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Inf Series, Summations with k, k^2 to get Summation of k(k+1)

  1. Nov 1, 2005 #1
    As I don't know how to use this latex coding here it goes....

    if I represent by E the sum of terms where k=1 and n is the unknown

    I need to use the formulae for Ek and Ek^2 to obtain a formula for Ek(k+1), by simplifying the algebra as much as possible.

    Can someone help with this please?
     
  2. jcsd
  3. Nov 1, 2005 #2
    Are you asking for:

    [tex]\sum_{k=1}^nk\left(k+1\right)[/tex]

    ?

    If so, note that k(k+1)=k2+k.
     
  4. Nov 1, 2005 #3
    Yes I am asking exactly that :-).

    Could someone start this problem, because I am stuck? Thank you :shy:
     
  5. Nov 1, 2005 #4
    You have seen the last line of the above reply right?
    So you have:
    [tex]\sum_{k=1}^nk\left(k+1\right)=\sum_{k=1}^n k^2+\sum_{k=1}^nk[/tex]
    that should take you off
     
  6. Nov 1, 2005 #5

    Ok so now I get

    = 1^2+1+2^2+2+3^3+3+.....+n^2+n

    and then what do I do?


    Is the answer then

    = n^2 + n
     
    Last edited: Nov 1, 2005
  7. Nov 2, 2005 #6
    If I understand your assignment correctly, you already have the formulas for the two expressions

    [tex]\sum_{k=1}^n k^2[/tex]
    [tex]\sum_{k=1}^nk[/tex]

    So just put a "+" between them :-) and simplify them even more if possible...

    But being foreign and all, i could have misinterpreted what you wrote, so please dont hate me if thats the case ;-)
     
  8. Nov 2, 2005 #7

    benorin

    User Avatar
    Homework Helper

    Here you go Natasha, (link)

    Here is a link to the answer I posted on your other thread:

    https://www.physicsforums.com/showthread.php?t=97842
     
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