Find the sum of first positive 1000 integers.

We need to find 1 + 2 + 3 + 4 + …… + 1000

The above series is an A.P. with first term a = 1, d = 1 and n = 1000.

By formula S_n = $\dfrac{n}{2}[2a + (n - 1)d]$

⇒ S₁₀₀₀ = $\dfrac{1000}{2}[2 \times 1 + (1000 - 1)1]$
⇒ S₁₀₀₀ = 500[2 + 999]
⇒ S₁₀₀₀ = 500 × 1001
⇒ S₁₀₀₀ = 500500.

Hence, the sum of first 1000 positive integers is 500500.