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How to calculate the sum (1+2)+(2+3)+(3+4)+...(2012+2013)+(2013+2014)?

1 Answer

Feb 19, 2018

$4056195$ $4056195$

Explanation:

This sum has $2013$ $2013$ bracketed terms, with average value:

$\frac{(1 + 2) + (2013 + 2014)}{2} = 2015$ $((1+2)+(2013+2014))/2 = 2015$

So the sum is:

$2013 \cdot 2015 = 2014^{2} - 1 = 4056195$ $2013 * 2015 = 2014^2-1 = 4056195$

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