To determine the sum of integers from 1 to 100 that are divisible by either 2 or 5, we need to follow these steps:
1. Identify the range of numbers: We're looking at numbers from 1 to 100 inclusive.
2. Define the criteria for selection:
- Numbers that are divisible by 2 (even numbers).
- Numbers that are divisible by 5.
3. List out numbers that meet the criteria:
- Numbers divisible by 2 in the range 1 to 100: [tex]\(2, 4, 6, 8, 10, \ldots, 100\)[/tex].
- Numbers divisible by 5 in the range 1 to 100: [tex]\(5, 10, 15, 20, 25, \ldots, 100\)[/tex].
4. Combine the numbers and remove duplicates:
- We note that some numbers are divisible by both 2 and 5 (e.g., 10, 20, 30, etc.).
- We include these numbers only once in our final calculation.
5. Add the qualifying numbers:
- Sum all the numbers that are divisible by either 2 or 5.
Calculating this sum thoroughly involves ensuring no double counting and including every number that meets at least one of the criteria.
Upon completion of these steps, the total sum of all numbers from 1 to 100 that are divisible by 2 or 5 is found to be:
[tex]\[ 3050 \][/tex]
Thus, the sum of integers from 1 to 100 that are divisible by 2 or 5 is 3050.
