Carl Freidrich Gauss was one of the great mathematicians of the 19th century.

Question

The story goes that when he was a young man he got in trouble at school. As a punishment, he was ordered to add up all the whole numbers from 1 to 100, a task the teacher thought would take several hours. He started on the problem and, to the teachers unbelief, was finished in just a few minutes. The teacher painstakingly added up all the numbers and found that Carl was correct.
Create a presentation that explains how Carl Gauss added up all of the numbers from 1 to 100 (you can find it on the internet).
Include an explanation in your presentation of what this has to do with the triangular numbers and the work you did in the the discussion group.
Remember to make your presentation look good and to be professional.
When you are done, share your presentation with me and post it to the Algebra Projects page on the website you made in your Student Orientation Course.

Answer 1

sum of 1+2+3+...+99+100 = 100(101)/2 = 50(101) = 5050

Gauss' formula is n(n+1)/2 for adding up the integers from 1 to n

construct pairs of the 1st and last integers,

then the 2nd and 2nd to last

then the 3rd and 3rd to last

etc.

each pair sums to 101. there are 100/2 such pairs

half as many pairs as integers

multiply 101 times 100/2 = 5050