Adding without a calculator

Algebra Level 2

Find the sum of 1 − 2 + 3 − 4 + 5 − ⋯ + 2017 = ? 1-2+3-4+5- \dots + 2017=?

1008 1007 1009 1005 1006

Hana Wehbi by Hana Wehbi , 51, USA

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2 solutions

S = 1 − 2 + 3 − 4 + 5 − 6 + 7 − ⋯ − 2016 + 2017 = 1 + 1 + 1 + 1 + ⋯ 1 ⏟ Number of 1 = 1008 = 1009 \begin{aligned} S & = 1 {\color{#3D99F6}- 2 + 3}{\color{#D61F06} - 4 + 5}{\color{#3D99F6}- 6 + 7} - \cdots - \color{#D61F06}2016 + 2017 \\ & = 1 \underbrace{ {\color{#3D99F6} + 1}{\color{#D61F06} + 1}{\color{#3D99F6} + 1} + \cdots \color{#D61F06}1}_{\text{Number of 1 = 1008}} \\ & = \boxed{1009} \end{aligned}

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Thank you.

Hana Wehbi - 3 years, 11 months ago

1 − 2 + 3 − 4 + ⋯ + 2017 = ( 1 − 2 ) + ( 3 − 4 ) + ( 5 − 6 ) + ⋯ + ( 2015 − 2016 ) + 2017 = ( − 1 ) + ( − 1 ) + ( − 1 ) + ⋯ + ( − 1 ) ⏟ 1008 number of ( − 1 ) + 2017 = − 1008 + 2017 = 1009 1-2+3-4+\dots+2017=(1-2)+(3-4)+(5-6)+\dots+(2015-2016)+2017=\underbrace{(-1)+(-1)+(-1)+\dots+(-1)}_{1008\space\text{number of}\space (-1)}+2017=-1008+2017=\boxed{1009}

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Thank you for sharing your solution.

Hana Wehbi - 3 years, 11 months ago

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