# The sum of integers from 1 to 200 that are divisible by 2 or 5 is

$\begin{array}{1 1} 10250 \\ 3050 \\ 14200 \\ 12100 \end{array}$

Explanation : Integers divisible by 2 are {2,4,6----------200}
$sum S_{1}=2(1+2+3+---------100)$
$\large\frac{2n(n+1)}{2}=\large\frac{100*101*2}{2}$
$S_{1}=10100$
Integers divisible by 5 are {5,10,15------200}
$S_{2}=5(1+2+3+-----40)$
$=5*\large\frac{40*41}{2}=4100$
$Integers\; divisible\;10\;are\;counted\;twice$
$we\; have \;to \;minus\; the\; sum$
$S_{3}=10+20+30+------200$
$=10(1+2+-------20)$
$=10*\large\frac{20*21}{2}=200$
$Sum\; of\; numbers\;from\;1\;to\;200\;that\;are\;divisible\;by\;2\;or\;5$
$=S_{1}+S_{2}-S_{3}$
$=10100+4100-2100$
$=12100.$
edited Jan 24, 2014