Question

The sum of integers from $1$ to $100$ that are divisible by $2$ or $5$ is _________.

Answer 1

The sum of integers from $1to100$ that are divisible by $2or5$ is

$S$ = sum of integers from $1to100$divisible by $2$ + sum of integers from $1to100$ divisible by $5$ - sum of integers from $1to100$ divisible by $10$

$=(2+4+6+...+100)+(5+10+15+...+100)-(10+20+...+100)$

$=\frac{50}{2}[2\times 2+49\times 2]+\frac{20}{2}[2\times 5+19\times 5]-\frac{10}{2}[2\times 10+9\times 10]$

$=2550+1050-550=3050$