Chapter 1.7, Problem 135PE

Expanding Your Skills

As a small child in school, the great mathematician Karl Friedrich Gauss (1777-1855) was said to have found the sum of the integers from 1 to 100 mentally:

$1+2+3+4+\cdots +99+100$

Rather than adding the numbers sequentially, he added the numbers in pairs:

$\left(1+99\right)+\left(2+98\right)+\left(3+97\right)+\cdots +100$

a. Use this technique to add the integers from 1 to 10.

b. Use this technique to add the integers from 1 to 20.