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

Integers divisible by 2 are \2,4,6,8,10 ... . .100\ Sum =2(1+2+ * s+50)=(2 x 50 x 51 / 2)=2550 Integers divisible by 5 are \5,10,15,20 ... 100\ Sum =5(1+2+3+ * s+20)=(5 x 20 x 21 / 2)=1050 Integers divisible by 10 are \10,20,30 ... 100\ Sum =10(1+2+ * s+10)=(10 x 10 x 11 / 2)=550 ∴ Sum of the integers from 1 to 100 That are divisible by 2 or 5=2550+1050- 550=3050.

The sum of integers from 1 to 100 that are divisible by... | 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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