Chapter 1.1, Problem 57E

In Exercises 57-60, identify the reasoning process, induction or deduction, in each example. Explain your answer.

It can be shown that

$1+2+3+\cdot \cdot \cdot +n=\frac{n(n+1)}{2}$

I can use this formula to conclude that the sum of the first one hundred counting numbers, $1+2+3+\cdot \cdot \cdot +100$, is

$\frac{100\left(100+1\right)}{2}=\frac{100\left(101\right)}{2}=50\left(101\right),\text{or}5050.$