Solve The Series

  • Thread starter klen
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  • #1
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[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
 

Answers and Replies

  • #2
tiny-tim
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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:
 
  • #3
HallsofIvy
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[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
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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