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!

Prove that for each n in N, 1^3+2^3+ +n^3=[n(n+1)/2]^2

  1. Aug 29, 2011 #1

    A93

    User Avatar

    prove that for each n in N, 1^3+2^3+...+n^3=[n(n+1)/2]^2
     
  2. jcsd
  3. Aug 29, 2011 #2

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    What did you try?? If you let us know where you're stuck, then we'll know how to help...
     
  4. Aug 29, 2011 #3

    A93

    User Avatar

    induction.
    my dumb butt got "lost" in the wanting to prove p(k+1) is true (if that even makes sense, lol)
     
  5. Aug 29, 2011 #4

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    and where are you stuck in induction??
     
  6. Aug 29, 2011 #5

    A93

    User Avatar

    the proving of p(k+1) is true.
    basically the area where for each k>=1, if P(k) is true, then p(k+1) is true.....basically the induction part, lol
     
  7. Aug 29, 2011 #6

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    Yes, so to show that p(k+1) is true, you need to prove that

    [tex]1^3+2^3+...+k^3+(k+1)^3=\left(\frac{(k+1)(k+2)}{2}\right)^2[/tex]

    Now, what happens if you appy "p(k) is true" on that??
     
  8. Aug 29, 2011 #7
    Induction has a few steps. Let's see if this clarifies them a bit,

    1) Base Case: Show that your summation formula works for k = 1 case (which is probably easiest here lol)

    2) Induction Case: Create an induction hypothesis. For this case, you assume that the kth case holds. In other words,

    [itex]\sum_{k=1}^{n}k^3=\left (\frac{n(n+1)}{2} \right )^2[/itex]

    is true. Now, show that the kth case implies the (k+1)th case. How do you think you can do this?
     
    Last edited: Aug 29, 2011
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Prove that for each n in N, 1^3+2^3+ +n^3=[n(n+1)/2]^2
  1. Prove n^3 <= 2^n (Replies: 9)

Loading...