Question

use the formula $s = \frac{n(n + 1)}{2}$ to find the sum of $1 + 2 + 3 + \dots + 470$.
$1 + 2 + 3 + \dots + 470 = \square$ (simplify your answer.)

Explanation:

Step1: Identify n value

Here, $n=470$ (last term of the sequence)

Step2: Substitute into sum formula

Substitute $n=470$ into $S=\frac{n(n+1)}{2}$
$$S=\frac{470\times(470+1)}{2}$$

Step3: Simplify the expression

First calculate $470+1=471$, then $\frac{470}{2}=235$
$$S=235\times471$$
$$S=235\times(400+70+1)=235\times400 + 235\times70 + 235\times1$$
$$S=94000+16450+235$$

Answer:

109685