Question

help me please

Answer 1

@Michele_Laino

Answer 2

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

Answer 3

wow thats confusing

Answer 4

your sum is composed by four terms, since k goes from 1 to 4

Answer 5

ok so what do i do

Answer 6

first term is:
\[\large {\left( { - 1} \right)^1}\left( {1 + 11} \right) = - 1 \cdot 12 = ...?\]

Answer 7

12 maybe

Answer 8

-1*12 = -12 right?

Answer 9

\[\Large {\left( { - 1} \right)^1}\left( {1 + 11} \right) = \left( { - 1} \right) \cdot 12 = - 12\]

Answer 10

ohh ok

Answer 11

second term is:
\[\Large {\left( { - 1} \right)^2}\left( {2 + 11} \right) = 1 \cdot 13 = ...?\]

Answer 12

13

Answer 13

correct!

Answer 14

third term is:
\[\large {\left( { - 1} \right)^3}\left( {3 + 11} \right) = \left( { - 1} \right) \cdot 14 = ...?\]

Answer 15

-14

Answer 16

yes!

Answer 17

finally, fourth term is:
\[\Large {\left( { - 1} \right)^4}\left( {4 + 11} \right) = 1 \cdot 15 = ...?\]

Answer 18

15

Answer 19

yes!

Answer 20

therefore your sum is:
\[ \Large - 12 + 13 - 14 + 15 = ...?\]

Answer 21

17

Answer 22

using the associative property of addition, we can rewrite that sum as below:
\[\large - 12 + 13 - 14 + 15 = \left( { - 12 - 14} \right) + \left( {13 + 15} \right) = ...?\]

Answer 23

-52

Answer 24

hint:
\[\large \begin{gathered}
- 12 + 13 - 14 + 15 = \left( { - 12 - 14} \right) + \left( {13 + 15} \right) = \hfill \\
\hfill \\
= - 26 + 28 = 28 - 26 = ...? \hfill \\
\end{gathered} \]

Answer 25

2

Answer 26

that's right!