Question

find the sum of: 1) the first 1000 positive integers and 2) the first n positive integer

Answer 1

1) sum of first 1000 positive integers = 1000(1000+1)/2 = 1000(1001)/2 = 500(1001) = 500500

2) sum of n positive numbers = n(n+1)/2

Answer 2

1) suppose S = 1 + 2 + 3 + ________+1000
using the formula Sn= n/2(a+l) for the sum of first and number of an aps, we have
S1000= 1000/2(1+1000)=500×1001=500500
2) suppose Sn= 1+2+3+_______________+n
here a=1 and the last term l is n
so, Sn= n(1+n)/2 or Sn= n(n+1)/2
therefore, the sum of first n positive integers is given by
Sn= n(n+1)/2