The Summation Shortcut

Algebra Level 2

$\large 1 + 2 + 3 + 4 +\cdots+ 999998 + 999999 + 1000000 = \, ?$

1 solution

Gian Tuazon
Mar 21, 2016

This is known as Gauss' Trick , and the formula is:

$\dfrac{(x(x+1))}{2}$

$\dfrac{(1000000(1000000+1))}{2}$

$\dfrac{(1000000)(1000001))}{2}$

$= 500000500000$

This could also work as a function, wherein:

$f(x) =$ $\dfrac{(x(x+1))}{2}$

In which you can replace $x$ with any integer, and the output with be the summation from $1$ to $x$

@Gian Tuazon , I think you interchanged x with 1 in your solution. (2nd step) [1000000(100000+1)]/2 {x = 1000000}

Angela Fajardo - 5 years, 2 months ago

Ah yes, i didn't notice, thanks for the fix!

Gian Tuazon - 5 years, 2 months ago