1. Not finding help here? Sign up for a free 30min 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!

Spivak's Calculus Chapter 2 Problem 1(ii)

  1. Jan 12, 2014 #1
    1. The problem statement, all variables and given/known data
    Prove the following formulas by induction.

    (ii) 13+...+n3= (1+...+n)2.

    I am starting Spivak's Calculus by myself, and I simply do not understand Spivak's proof for the sum of the cubes equaling the square of the sum, exercise 1 (ii) of chapter 2 in his third edition. I tried to attach his proof to this thread. The only step I cannot figure out is the first, where (1+...+k+[k+1])2 = (1+...+k)2+2(1+...+k)(k+1)+(k+1)2.

    I have already worked through problem 1 (i), so I understand everything that follows the first line of the proof. But how/why does the square of the sums expand this way once induction is applied? Please help!
     

    Attached Files:

    Last edited: Jan 12, 2014
  2. jcsd
  3. Jan 12, 2014 #2

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    What is (a + b)2 ?

    Now let a = 1 + 2 +3 + ... + k

    and b = (k + 1)
     
  4. Jan 12, 2014 #3
    Oh bother...

    thank you
     
  5. Jan 12, 2014 #4

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    With all those + ... + k ... it can be hard to see.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Spivak's Calculus Chapter 2 Problem 1(ii)
Loading...