Question

Find the sum of (i) the first 1000 positive integers (ii) the first n positive integers.​

Answer 1

Answer:

(i) Let S = 1 + 2 + 3 + . . . + 1000 Using the formula Sn =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 Sn = 1 + 2 + 3 + . . . + n Here a = 1 and the last term l is n.

Sn=n/2[a+l]

n/2[1+n]

Sn=(n²+n)/2

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