Question

Find the sum of the first 1000 positive integers

Answer 1

Answer:

500500

Step-by-step explanation:

1+2+3+4+5......1000

As (1000+1)=1001

(999+2) = 1001

(998+3) = 1001

etc....

We conclude that the sum if all positive integers from 1 to 1000 = 1001 × 1/2(1000)

1001×500 = 500500

Answer 2

n = 1000 , d = 1 , a = 1

$</strong><strong>S</strong><strong>um_{n} = \frac{n}{2} (2a + (n - 1)d) \\ \\ </strong><strong>S</strong><strong>um_{1000} = \frac{1000}{2} (2 \times 1 + (1000 - 1) \times 1) \\ \\ </strong><strong>S</strong><strong>um_{1000} = 500 \times 1001 \\ \\ </strong><strong>S</strong><strong>um_{1000} = 500500$