Question

find the difference between the sum of all even numbers from 1 to 1000 and the sum of all odd numbers from 1 to 1000​

Answer 1

Step-by-step explanation:

the sum of all even no from 1 to 1000 is

250500

and the sum of all odd no from 1 to 1000 is

25000

Answer 2

Difference between the sum of even and sum of odd numbers from 1 to 1000 is 500.

• To find the sum of even numbers from 1 to 1000 we see that the resulting numbers are in arithmetic progression
• For this even series first term(a) will be 2 and the last term will be 1000
• To calculate the number of terms we have tn=a + (n-1)d

1000 = 2 + (n-1)2

n= 500

• Sum of even numbers can calculated as $\frac{n}{2}(a + l)$

sum of even numbers = 250500

• Similarly calculating odd numbers from  1 to 1000
• Here first term = 1 and last term = 999 and number of terms =500

• Now sum of odd number is $\frac{n}{2}(a + l)$

sum of odd numbers = 25000

Calculating the difference between both the sums = 250500 - 250000 = 500