The sum of integers from 1 to 100 that are di | vedclass

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(B) Let $S_2$ be the sum of integers divisible by $2$,$S_5$ be the sum of integers divisible by $5$,and $S_{10}$ be the sum of integers divisible by b

Vedclass · Accepted Answer

$3050$

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(B) Let $S_2$ be the sum of integers divisible by $2$,$S_5$ be the sum of integers divisible by $5$,and $S_{10}$ be the sum of integers divisible by both $2$ and $5$ (i.e.,divisible by $10$).$S_2 = 2 + 4 + \dots + 100 = \frac{50}{2}(2 + 100) = 25 	imes 102 = 2550$.$S_5 = 5 + 10 + \dots + 100 = \frac{20}{2}(5 + 100) = 10 	imes 105 = 1050$.$S_{10} = 10 + 20 + \dots + 100 = \frac{10}{2}(10 + 100) = 5 	imes 110 = 550$.By the Principle of Inclusion-Exclusion,the required sum is $S_2 + S_5 - S_{10} = 2550 + 1050 - 550 = 3050$.

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

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