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Compute 1 - 2 + 3 - 4 +... + 2005 - 2006 + 2007 - 2008 + 2009 - 2010.

 Nov 4, 2021
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Compute 1 - 2 + 3 - 4 +... + 2005 - 2006 + 2007 - 2008 + 2009 - 2010.

 

Hello Guest!

 

The sum of a finite arithmetic sequence is the number of terms multiplied by the arithmetic mean of the first and the last term.

 

\(s_n=n\cdot \dfrac{a_1+a_n}{2}\)

                      n            \(a_1\)       \(a_n\)

\(s_{2009}= \dfrac{1+2009}{2}\cdot \dfrac{1+2009}{2} = 1005\cdot \dfrac{1+2009}{2}=1010025\)

\(s_{-2010}= \dfrac{2+2010}{2}\cdot \dfrac{-2+(-2010)}{2}=1006\cdot \dfrac{-2+(-2010)}{2} =-1012036\)

\(s_n=s_{2009}+s_{-2010}=1010025+(-1012036)\)

\(s_n=-2011\)

laugh  !

 Nov 5, 2021

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