The sum of the integers from 1 to 100 which a | vedclass

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(D) Let $S$ be the sum of integers from $1$ to $100$: $S = \frac{100}{2}(1 + 100) = 5050$.Let $S_1$ be the sum of integers divisible by $3$: $S_1 = 3

Vedclass · Accepted Answer

$2632$

Vedclass · Answer

(D) Let $S$ be the sum of integers from $1$ to $100$: $S = \frac{100}{2}(1 + 100) = 5050$.Let $S_1$ be the sum of integers divisible by $3$: $S_1 = 3 + 6 + ... + 99 = 3(1 + 2 + ... + 33) = 3 	imes \frac{33 	imes 34}{2} = 1683$.Let $S_2$ be the sum of integers divisible by $5$: $S_2 = 5 + 10 + ... + 100 = 5(1 + 2 + ... + 20) = 5 	imes \frac{20 	imes 21}{2} = 1050$.Let $S_3$ be the sum of integers divisible by both $3$ and $5$ (i.e.,divisible by $15$): $S_3 = 15 + 30 + ... + 90 = 15(1 + 2 + ... + 6) = 15 	imes \frac{6 	imes 7}{2} = 315$.The sum of integers divisible by $3$ or $5$ is $S_1 + S_2 - S_3 = 1683 + 1050 - 315 = 2418$.The required sum is $S - (S_1 + S_2 - S_3) = 5050 - 2418 = 2632$.

The sum of the integers from $1$ to $100$ which are not divisible by $3$ or $5$ is

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