The sum of integers from 1 to 100 that are divisible by 2 or 5 is: Sequence & Series (Mathematics)

Integers divisible by 2 are $\{2,4,6,8,10 \ldots . .100\}\\$ { Sum }= $2(1+2+\cdots+50)=\frac{2 \times 50 \times 51}{2}=2550\\$ Integers divisible by 5 are $\{5,10,15,20 \ldots 100\}\\$ { Sum } $=5(1+2+3+\cdots+20)=\frac{5 \times 20 \times 21}{2}=1050\\$ Integers divisible by 10 are $\{10,20,30 \ldots 100\}\\$ { Sum }= $10(1+2+\cdots+10)=\frac{10 \times 10 \times 11}{2}=550\\$ ∴ Sum of the integers from 1 to 100 $\\$ That are divisible by 2 or 5=2550+1050- 550=3050.

Explanation

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