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How to write another expression (for n) when given a series sum?

  1. Mar 3, 2010 #1
    1. The problem statement, all variables and given/known data
    Sorry if the question sounds a bit off, i wasnt quite sure how to word it.

    My math question is: given the expression Sn=n^2 + 2n, determine an expression, in simplified form, for Sn-1 in terms of n.

    2. Relevant equations

    NA (i dont think there are any equations for this)

    3. The attempt at a solution

    I honestly dont know how to go about this properly but here's what ive done:

    First three terms are 3, 8 and 15. All of which have a different 'common ratio' when 8 is divided by 3, its 2.67 but when 15/8 its 1.875?
    Which confuses me further, and as for the original question, no idea how to proceed.

    Any help is much appreciated, thanks.
  2. jcsd
  3. Mar 3, 2010 #2
    try substituting n-1 for in in the expression for S(n) and then simplifying the result.
  4. Mar 3, 2010 #3


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    Homework Helper

    Well of course the ratios aren't the same! It's a quadratic! Not a linear equation...
  5. Mar 4, 2010 #4
    Its not a case of dividing the n-1 by n as it is a ascending arithmetic method as the difference keeps increasing by 2:

    1 2 3
    3 8 15

    8-3 = 5, 15-8 = 7, so the next difference will equal 9 then 11 and so on an so forth, so your equation is essentially using the "box" number, 1 2 3, to get the actual number in the formula

    So if Sn=n^2 + 2n, Sn-1 means you have to rewrite the formula in terms of the previous number
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