Sum of all Natural Numbers between 500 and 1000 Divisible by 13

To find the sum of all natural numbers between 500 and 1000 that are divisible by 13, we can follow a step-by-step approach.

Step 1: Find the first number divisible by 13 within the given range
To determine the first number divisible by 13, we need to find the smallest multiple of 13 greater than or equal to 500. We can use the formula:

First number = 13 * (Smallest integer greater than or equal to 500/13)

By substituting the values, we have:
First number = 13 * (39) = 507

Step 2: Find the last number divisible by 13 within the given range
Similarly, we need to find the largest multiple of 13 that is less than or equal to 1000. We can use the formula:

Last number = 13 * (Largest integer less than or equal to 1000/13)

By substituting the values, we have:
Last number = 13 * (76) = 988

Step 3: Find the number of terms in the series
To find the number of terms in the series, we can use the formula:

Number of terms = (Last number - First number)/13 + 1

By substituting the values, we have:
Number of terms = (988 - 507)/13 + 1 = 35

Step 4: Calculate the sum of the series
To find the sum of the series, we can use the formula:

Sum = (Number of terms * (First number + Last number))/2

By substituting the values, we have:
Sum = (35 * (507 + 988))/2 = 35 * 1495/2 = 26,075

Therefore, the sum of all natural numbers between 500 and 1000 that are divisible by 13 is 26,075.