en.wikipedia.org/wiki/Triangular_number

A triangular number or triangle number counts the objects that can form an equilateral triangle, ... Carl Friedrich Gauss is said to have found this relationship in his early youth, by multiplying n/2 pairs of numbers in the ... Most simply, the sum of two consecutive triangular numbers is a square number, with the sum being the ...

betterexplained.com/articles/techniques-for-adding-the-numbers-1-to-100

Manual addition was for suckers, and Gauss found a formula to sidestep the ... The above method works, but you handle odd and even numbers differently.

mathcentral.uregina.ca/qq/database/qq.02.06/jo1.html

In elementary school in the late 1700's, Gauss was asked to find the sum of the numbers from 1 to 100. The question was assigned as “busy work” by the teacher ...

nzmaths.co.nz/gauss-trick-staff-seminar

Let's go for adding up Gauss' numbers, all the whole numbers from 1 to 100. .... Method 1: We could write out the numbers from 8 to 93 in the normal order and .... of numbers where there is a common difference between consecutive numbers.

superm.math.hawaii.edu/_lessons/k_five/gauss_addition.pdf

Students will learn how to find the sum of consecutive, positive integers ... Try adding up all the numbers between 1 and 23 by copying Gauss' method before.

nrich.maths.org/2478

Find out how Carl Gauss responded when he was asked to do just that. ... Gauss could have used his method to add all the numbers from 1 to any number - by ... all use similar clever counting to come up with a formula for adding numbers.

math.stackexchange.com/questions/50485/sum-of-n-consecutive-numbers

Jul 9, 2011 ... Is there a shortcut method to working out the sum of n consecutive positive integers? Firstly, starting at 1...1+2+3+4+5=15. Secondly, starting at ...