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!

Question about this proof

  1. Sep 14, 2011 #1
    1. The problem statement, all variables and given/known data


    Prove that for all integers [tex]n \geq 1[/tex], one has

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

    (1) S(1) = 1, true

    (2) Let n = k + 1

    [tex]1 + 2 + ... + k + (k + 1) = \frac{(k+`1)(k + 2)}{2}[/tex]





    3. The attempt at a solution

    Why is the last series

    [tex]1 + 2 + ... + k + (k +1)[/tex] instead of [tex]1 + 2 +...+ (k + 1)[/tex]?
     
  2. jcsd
  3. Sep 14, 2011 #2

    rock.freak667

    User Avatar
    Homework Helper

    Because the (k+1)th term to each side of the equation, which happens to be 'k+1'. The right side simplifies to (k+1)(k+2)/2
     
  4. Sep 14, 2011 #3

    Mark44

    Staff: Mentor

    You're skipping a step here, again. There are three things you have to establish in an induction proof:
    1) Base case (typically for n = 1)
    2) The induction hypothesis - you assume that the statement is true for n = k
    3) The induction step (I think that's what it's called) - you use the statement for n = k to show that the statement is also true for n = k + 1.
    These two are exactly the same. Each one represents the sum of the integers from 1 through k + 1. The first expression explicitly shows k, and the other one doesn't, but we can infer that the second expression doesn't skip from k - 1 to k + 1 in the sum.
     
  5. Sep 14, 2011 #4
    Is it bad that I don't show it?
     
  6. Sep 14, 2011 #5

    Mark44

    Staff: Mentor

    If your professor is a stickler, or if he/she isn't convinced that you know what it should be, it is.

    In an induction proof, you should ALWAYS write down your induction hypothesis.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Question about this proof
  1. Question about proof (Replies: 2)

  2. Question About Proof (Replies: 9)

  3. Question about Proof (Replies: 1)

  4. Question about a proof (Replies: 15)

Loading...