Explanation

(b)
The sum of integers from 1 to 100 that are divisible by 2 or 5 $=$ sum of series divisible by 2+ sum of series divisible by 5$- \$sum of series divisible by 2 ad 5.
$= (2 + 4 + 6 + ... + 100) + (5 + 10 + 15 + ... + 100) - (10 + 20 + 30 + ... + 100)$
$= \frac{50}{2}\left\{ 2 \times 2 + (50 - 1)2 \right\} + \frac{20}{2}\left\{ 2 \times 5 + (20 - 1)5 \right\} - \frac{10}{2}\{ 10 \times 2 + (10 - 1)10\}$
$= 25(102) + 10(105) - 5(110)$
$= 2550 + 1050 - 550 = 3050$