Find the sum of first 1000 positive integers.

Required arithmetic progression is 1, 2, 3, …, 1000
Here, first term a= 1 and common difference d = 1.

Since the sum of n terms is
S_{n =}

Where,

a = First term of AP
d = Common difference of AP
and no of terms is ‘n’

S_{1000 =}
= 500 [ 2 + 999]

= 500 × 1001
= 500500

Hence, Sum of first 1000 positive integers is 500500.