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Spivak's Calculus Ch.2 Problem 2(i)

  1. Mar 18, 2016 #1
    1. The problem statement, all variables and given/known data
    Find a formula for Σ(2i-1) = 1+3+5+...+(2n-1)

    Hint: What does the expression have to do with 1+2+3+...+2n?

    2. Relevant equations


    3. The attempt at a solution
    I have tried to solve this on my own for about a day now, and I am having trouble understanding the significance of the hint. I don't want an answer, just advice on how to connect the hint and the original expression.
     
  2. jcsd
  3. Mar 18, 2016 #2
    Hint: let ##S = 1 + 2 + ... + 2n## and ##Y = 1 + 3 + 5 + ... + (2n - 1)##

    Then what is ##S - Y##?
     
  4. Mar 18, 2016 #3

    Ray Vickson

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    Also: how can you find ##S-Y## in terms of ##n##?
     
    Last edited: Mar 19, 2016
  5. Mar 19, 2016 #4
    Thanks guys, i finally had an epiphany earlier today with your hints.
     
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