Question

Find the sum of :

(i) the first 1000 positive integers (ii) the first n positive integers

Answer 1

(i) Let S = 1 + 2 + 3 + . . . + 1000

Using the formula S_n =n/2(a+1) for the sum of the first n terms of an AP, we have

S1000=1000/2(1+1000)=500x1001=500500

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

(ii) Let S_n = 1 + 2 + 3 + . . . + n

Here a = 1 and the last term l is n.