Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Mathematical Induction

  1. Jun 17, 2008 #1

    Blank101

    User Avatar

    Prove that S1, S2, S3 are true statements
    1+3+5+....+(2n-1)=n^2


    S1=1= (2(1)-1) = 1^2 True
    S2=1+3 = (2(3)-1) = 5 which cannot= to the sum of our first 2 integers, which will make it false!!!
    S3=1+3+5 = (2(5)-1) = 3^2 True

    The problem is with S2 the book gave me an answer of 4=4 which is 2^2!!!
    It also shows a different formula (n-1) = n^2

    In my understanding of The mathematical induction a formula is usually given to prove an x number of integers, all those integers being proven true does not mean will be the same to all integers from the sequence. Thats when K+1 substitution comes in.

    Can someone help me i know is a simple mistake but i cant just see why s2 is coming that way!!!!

    Thanx
     
    Blank101, Jun 17, 2008
  2. jcsd
    Phys.org - latest science and technology news stories on Phys.org
  3. Jun 17, 2008 #2

    rock.freak667

    User Avatar
    Homework Helper

    1+3+5+....+(2n-1)=n^2

    the (2n-1) gives the nth term.
    So the second term is 2(2)-1=3 (as seen in the series)

    and so S2=1+3=4 (LHS)
    and S2=2^2 (RHS)

    LHS=RHS so it's true
     
    rock.freak667, Jun 17, 2008
  4. Jun 17, 2008 #3

    Defennder

    User Avatar
    Homework Helper

    That's an odd "proof" of induction. You've verified it for S1, S2, S3, but these are just particular instances of the problem you're purportedly trying to prove by induction, not the general "k+1" case.
     
    Defennder, Jun 17, 2008
  5. Jun 19, 2008 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    I don't believe he is claiming that as a "proof". He was asserting that the statement was not true. It is true, of course, he simply did not understand what the formula said:

    No, the statement does NOT say 1+ 3= 2(3)- 1, it says 1+ 3= 1+ (2(2)-1)= 2^2. It is the last integer that is "2n- 1", not the sum.

    In fact, your statement about S3 is incorrect: 1+ 3+ 5= 1+ [2(2)- 1]+ [2(3)-1]= 3^2 is what it says.
     
    HallsofIvy, Jun 19, 2008
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Mathematical Induction

  1. Mathematical Induction (Replies: 17)

  2. Mathematical induction (Replies: 24)

  3. Mathematical induction (Replies: 7)

  4. Mathematical Induction (Replies: 15)

  5. Mathematical induction (Replies: 0)

Loading...