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Solve The Series

  1. Jun 4, 2013 #1
    [tex] S_n = \sum_{k=1}^ {4n} {(-1)^\frac{k(k+1)}{2}} {k^2} [/tex].

    Then Sn can take what values among:
    1056, 1088, 1120, 1332
  2. jcsd
  3. Jun 4, 2013 #2


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    hi klen! :wink:

    simplest way is probably to do the sum for 4m-3,4m-2,4m-1,4m (only) first …

    what do you get? :smile:
  4. Jun 4, 2013 #3


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    Did you, for example, notice that every time n increases by 1, the sum has 4 new terms, two negative and two positive? Do you notice that for n= 1, so there are 4 terms, the sum is 20= 4(5) and when n= 2, so there are 8 terms, the sum is 72= 8(9)?
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