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Compute the value of 1-2+3-4+...+2019-2020+2021

 May 18, 2022
 #1
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1 - 2 + 3 - 4 + ... + 2019 - 2020 + 2021 = 1007.

 May 18, 2022
 #2
avatar+26287 
+2

Compute the value of
\(1 - 2 + 3 - 4 + \dots + 2019 - 2020 + 2021\).

 

\(\begin{array}{|rcll|} \hline s &=& 1 - 2 + 3 - 4 + \dots + 2019 - 2020 + 2021 \\ s&=& 2021 - 2020 +2019 - \dots -4+3-2+1 \\ \hline 2s &=& 2022-2022+2022-2022 + \dots + 2022-2022+2022 \\ 2s &=& 0+0+ \dots +0+2022 \\ 2s &=& 2022 \\ s &=& 1011 \\ \hline \end{array}\)

 

\(1 - 2 + 3 - 4 + \dots + 2019 - 2020 + 2021 = \mathbf{1011} \)

 

laugh

 May 18, 2022
 #3
avatar+9457 
0

heureka posted a great solution, so I will post a different one.

 

\(\quad1 - 2 + 3 - 4 + \cdots + 2019 - 2020 + 2021\\ =(1 - 2) + (3 - 4) + \cdots + (2019 - 2020) + 2021\\ = \underbrace{(-1) + (-1) + \cdots + (-1)}_{1010\text{ times}} + 2021\\ =-1010 + 2021\\ = 1011\)

 May 18, 2022

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