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: Adding consecutive squares?

  1. Oct 2, 2005 #1
    ok, i need to derive a forumla that will add the consecutive squares of n numbers.

    for example [tex]1^2 + 2^2 + 3^2 + ... + (n-2)^2 + (n-1)^2 + (n)^2[/tex]

    I have worked on this problem for quite some time and havent been able to come up with anything.

    I do know that the sum of consecutive numbers starting at one is

    [tex]\frac{n}{2} (n+1)[/tex]

    A very detailed explanation would be excellent as that's what my professor wants.
    Last edited: Oct 2, 2005
  2. jcsd
  3. Oct 2, 2005 #2
    [tex]S(n) = \frac{n(n+1)(2n+1)}{6}[/tex].

    You should be able to prove it by induction.
  4. Oct 2, 2005 #3
    what's induction?

    can you explain how you came to the answer?
  5. Oct 2, 2005 #4
    inductions like this...
    prove it works for 1
    assume it works for n
    and prove it works for n+1
  6. Oct 2, 2005 #5
    s=summation of t
    we will get s
  7. Oct 2, 2005 #6
    Dr. Math has answered a lot of questions concerning the sum of consecutive squares here. He explains that there are several ways to derive the formula.
  8. Oct 2, 2005 #7
    ok, so i understand what inductions are, but can you explain how you got to the proof for the sum of the sequence of [tex]n^2[/tex]

    *** edit *** i just posted the above before reading the previous 3 posts. i'll go ahead and read dr math's explanation and then come back to this :)
  9. Oct 2, 2005 #8

    i need to derive the forumula... not prove it :)
  10. Oct 2, 2005 #9
    Sequence of Differences. Search here or Dr. Math, there are explanations at both places.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook