Question

find the sum of all the integers from 1 to 1000.

Answer 1

sum of all the integers from 1 to 1000,
S = n/2 (a+an) = 1000/2 (1+1000) = 500×1001 = 500500

Answer 2

500500

To Find:

The Sum Of All Integers From 1 to 1000

Formula used to calculate the sum of n terms in an AP:

Sn = n/2 (2a + (n - 1) d)

Here the sum of n terms is going to be the sum of all the integers from 1 to 1000.

n = 1000

a = 1

d = 1

Now substituting all the values into the sum of n terms formula we get:

= 1000 / 2 (2 x 1 + (1000 - 1) x 1

= 500 (2 + 999)

= 500 x 1001

= 500500

Therefore, the sum of all the integers from 1 to 1000 is 500500.