anonymous
  • anonymous
help me please
Mathematics
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anonymous
  • anonymous
help me please
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
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anonymous
  • anonymous
Michele_Laino
  • Michele_Laino
we can make explicit the sum notation like below: \[\large \begin{gathered} \sum\limits_{k = 1}^4 {{{\left( { - 1} \right)}^k}\left( {k + 11} \right) = } {\left( { - 1} \right)^1}\left( {1 + 11} \right) + {\left( { - 1} \right)^2}\left( {2 + 11} \right) + \hfill \\ \hfill \\ + {\left( { - 1} \right)^3}\left( {3 + 11} \right) + {\left( { - 1} \right)^4}\left( {4 + 11} \right) = ... \hfill \\ \end{gathered} \]

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anonymous
  • anonymous
wow thats confusing
Michele_Laino
  • Michele_Laino
your sum is composed by four terms, since k goes from 1 to 4
anonymous
  • anonymous
ok so what do i do
Michele_Laino
  • Michele_Laino
first term is: \[\large {\left( { - 1} \right)^1}\left( {1 + 11} \right) = - 1 \cdot 12 = ...?\]
anonymous
  • anonymous
12 maybe
Michele_Laino
  • Michele_Laino
-1*12 = -12 right?
Michele_Laino
  • Michele_Laino
\[\Large {\left( { - 1} \right)^1}\left( {1 + 11} \right) = \left( { - 1} \right) \cdot 12 = - 12\]
anonymous
  • anonymous
ohh ok
Michele_Laino
  • Michele_Laino
second term is: \[\Large {\left( { - 1} \right)^2}\left( {2 + 11} \right) = 1 \cdot 13 = ...?\]
anonymous
  • anonymous
13
Michele_Laino
  • Michele_Laino
correct!
Michele_Laino
  • Michele_Laino
third term is: \[\large {\left( { - 1} \right)^3}\left( {3 + 11} \right) = \left( { - 1} \right) \cdot 14 = ...?\]
anonymous
  • anonymous
-14
Michele_Laino
  • Michele_Laino
yes!
Michele_Laino
  • Michele_Laino
finally, fourth term is: \[\Large {\left( { - 1} \right)^4}\left( {4 + 11} \right) = 1 \cdot 15 = ...?\]
anonymous
  • anonymous
15
Michele_Laino
  • Michele_Laino
yes!
Michele_Laino
  • Michele_Laino
therefore your sum is: \[ \Large - 12 + 13 - 14 + 15 = ...?\]
anonymous
  • anonymous
17
Michele_Laino
  • Michele_Laino
using the associative property of addition, we can rewrite that sum as below: \[\large - 12 + 13 - 14 + 15 = \left( { - 12 - 14} \right) + \left( {13 + 15} \right) = ...?\]
anonymous
  • anonymous
-52
Michele_Laino
  • Michele_Laino
hint: \[\large \begin{gathered} - 12 + 13 - 14 + 15 = \left( { - 12 - 14} \right) + \left( {13 + 15} \right) = \hfill \\ \hfill \\ = - 26 + 28 = 28 - 26 = ...? \hfill \\ \end{gathered} \]
anonymous
  • anonymous
2
Michele_Laino
  • Michele_Laino
that's right!

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