Question

Find the sum of integers from $1$ to $100$ which are divisible by $2$ or $5$

Answer 1

Sum of integers which are divisible by $2$ or $5$ is
$S=(2+4+6+8+10+12+..................+100)+(5+15+25+\mathrm{35.......}+95)$
$=2(1+2+3+.......................50)+5(1+3+7+...........+19)$
$=2\left(\frac{50\times 51}{2}\right)+5\left({10}^2\right)$
(since, Sum of first $n$ integers $=\frac{n(n+1)}{2}$
and Sum of first $n$ odd numbers $=n^2$ )
$\therefore S=2550+500=3050$