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anonymous
 one year ago
help me please
anonymous
 one year ago
help me please

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Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1we can make explicit the sum notation like below: \[\large \begin{gathered} \sum\limits_{k = 1}^4 {{{\left( {  1} \right)}^k}\left( {k + 11} \right) = } {\left( {  1} \right)^1}\left( {1 + 11} \right) + {\left( {  1} \right)^2}\left( {2 + 11} \right) + \hfill \\ \hfill \\ + {\left( {  1} \right)^3}\left( {3 + 11} \right) + {\left( {  1} \right)^4}\left( {4 + 11} \right) = ... \hfill \\ \end{gathered} \]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1your sum is composed by four terms, since k goes from 1 to 4

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1first term is: \[\large {\left( {  1} \right)^1}\left( {1 + 11} \right) =  1 \cdot 12 = ...?\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.11*12 = 12 right?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1\[\Large {\left( {  1} \right)^1}\left( {1 + 11} \right) = \left( {  1} \right) \cdot 12 =  12\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1second term is: \[\Large {\left( {  1} \right)^2}\left( {2 + 11} \right) = 1 \cdot 13 = ...?\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1third term is: \[\large {\left( {  1} \right)^3}\left( {3 + 11} \right) = \left( {  1} \right) \cdot 14 = ...?\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1finally, fourth term is: \[\Large {\left( {  1} \right)^4}\left( {4 + 11} \right) = 1 \cdot 15 = ...?\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1therefore your sum is: \[ \Large  12 + 13  14 + 15 = ...?\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1using the associative property of addition, we can rewrite that sum as below: \[\large  12 + 13  14 + 15 = \left( {  12  14} \right) + \left( {13 + 15} \right) = ...?\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1hint: \[\large \begin{gathered}  12 + 13  14 + 15 = \left( {  12  14} \right) + \left( {13 + 15} \right) = \hfill \\ \hfill \\ =  26 + 28 = 28  26 = ...? \hfill \\ \end{gathered} \]
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