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Algebra Level 1

Evaluate the sum,

1 − 2 + 3 − 4 + 5 − 6 + ⋯ + 2015 − 2016. 1-2+3-4+5-6+\cdots+2015-2016 .

2016 2016 1008 1008 2015 2015 − 1008 - 1008 0 0

Hana Wehbi by Hana Wehbi , 51, USA

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1 solution

Chew-Seong Cheong
Nov 18, 2016

S = 1 − 2 + 3 − 4 + 5 − 6 + . . . + 2015 − 2016 = ( 1 − 2 ) + ( 3 − 4 ) + ( 5 − 6 ) + . . . + ( 2015 − 2016 ) = − 1 − 1 − 1 − . . . − 1 ⏟ 1008 × ( − 1 ) = − 1008 \begin{aligned} S & = 1-2+3-4+5-6+...+2015-2016 \\ & = (1-2)+(3-4)+(5-6)+...+(2015-2016) \\ & = \underbrace{-1-1-1-...-1}_{1008 \times (-1)} \\ & = \boxed{-1008} \end{aligned}

7 Helpful 0 Interesting 0 Brilliant 0 Confused

Thank you for the nice solution.

Hana Wehbi - 4 years, 6 months ago

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