Question

What is the sum of integers from $1to100$divisible by$2or5$?

Answer 1

Determine the sum of integers between $1to100$divisible by$2or5$.

The numbers between $1and100$ that are divisible by $2$ are$2,4,6,8,\dots ..,100$

$2+4+6+8+\dots .+100$

Calculate the sum:

$$\begin{gathered} \frac{50}{2}(2+100)=\frac{50}{2}\times 102 \\ \Rightarrow =25\times 102 \\ \Rightarrow =2550 \end{gathered}$$

The numbers between$1and100$ that are divisible by $5$ are $5,10,15,20,\dots \dots .,100$

$5+10+15+\dots ..+100$

Calculate the sum:

$$\begin{gathered} \frac{20}{2}(5+100)=\frac{20}{2}\times 105 \\ \Rightarrow =10\times 105 \\ \Rightarrow =1050 \end{gathered}$$

The numbers between$1and100$ that are divisible by $10$ are $10+20+\dots .+100$

Calculate the sum:

$$\begin{gathered} \frac{10}{2}(10+100)=\frac{10}{2}\times 110 \\ \Rightarrow =5\times 110 \\ \Rightarrow =550 \end{gathered}$$

Final sum: $2550+1050-550=3050$

Determine the sum of integers between $1to100$divisible by$2or5$ is $"3050"$