Sum of all integers from [1-100=100(1+100)]/2=5050


no of terms from 1-100 which are divisible by 2 are
:2,4,6, up to 100
100=2+(n-1)2
=>n=50


sum of all integers which are divisible by 2
=[50(2+100)]/2=2550


no of terms which are divisible by 5 are
5,10,15 up to 100
100=5+(n-1)5
=>n=20


sum of all integers divisible by 5 between 1-100= [20(5+100)]/2=1050


terms which are multiplied by both 2 and 5
are 10,20,30,40,50,60,70,80,90,100
sum of these terms =550

hence sum of integers which are not divisible by 2 and 5 is
5050-2550-1050+550=2000

Sum of Integers Not Divisible by 2 or 5

To find the sum of all integers from 1 to 100 that are neither divisible by 2 nor 5, we need to follow a step-by-step approach. Let's break down the problem into smaller parts and explain each step in detail:

1. Finding the Numbers
- We need to identify the integers from 1 to 100 that are not divisible by 2 or 5.
- Divisibility by 2: Integers divisible by 2 leave no remainder when divided by 2. So, we need to exclude all even numbers.
- Divisibility by 5: Integers divisible by 5 leave no remainder when divided by 5. Therefore, we need to exclude all numbers ending with 0 or 5.

2. Identifying the Numbers
- We can start by listing the numbers from 1 to 100.
- Then, we exclude all even numbers by removing all numbers divisible by 2.
- Next, we exclude numbers ending with 0 or 5 by removing all numbers divisible by 5.

3. Calculating the Sum
- Once we have identified the required numbers, we can sum them up to find the total.
- We can use a simple formula to calculate the sum of consecutive integers.
- The formula for the sum of consecutive integers is: sum = (n/2) * (first number + last number), where n is the count of numbers.
- In this case, the count of numbers is the total number of integers not divisible by 2 or 5.

4. Applying the Formula
- Using the formula, we can substitute the values.
- The count of numbers can be found by subtracting the excluded numbers from the total count of integers (100).
- The first number would be the smallest number in the list, which is 1.
- The last number would be the largest number in the list, which is the count of numbers itself.

5. Calculating the Sum
- After substituting the values into the formula, we can calculate the sum.

In conclusion, by following the steps mentioned above, we can find the sum of all integers from 1 to 100 that are neither divisible by 2 nor 5. Remember to exclude all even numbers and numbers ending with 0 or 5, and then use the sum formula to calculate the final result.