anonymous
  • anonymous
Finding the indicated sum ,
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
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whpalmer4
  • whpalmer4
This one can be solved without any cleverness. \[\sum_{k=1}^{4}(-1)^k(k+11) =\]\[(-1)^1(1+11)+(-1)^2)(2+11)+(-1)^3)(3+11)+(-1)^4(4+11) =\]
whpalmer4
  • whpalmer4
Now why did I stick in those unwanted )'s? \[(-1)^1(1+11)+(-1)^2(2+11)+(-1)^3(3+11)+(-1)^4(4+11) =\] For odd k, \((-1)^k = -1\) For even k, \((-1)^k = 1\) -(1+11)+(2+11)-(3+11)+(4+11) = all the alternating of signs cancels out the 11s, so it's just -1 + 2 - 3 + 4 = 2

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anonymous
  • anonymous
How did you get the -1+2-3+4?
anonymous
  • anonymous
When I solved it I didnt get none of that, maybe I did it wrong?
whpalmer4
  • whpalmer4
\[-(1+11)+(2+11)-(3+11)+(4+11) = -1 -11 + 2 + 11 - 3 - 11 + 4 + 11\] The alternating -11 + 11 sum to 0, leaving -1 + 2 - 3 + 4
anonymous
  • anonymous
Ah okay, I get it

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