Question 853347
the sum of the first n positive integers is given by the formula
n(n+1) / 2
note that if n = 1, then
1(1+1) / 2 = 2/2 = 1
now assume that the formula
n(n+1) / 2 is true for n > 1
we need to show that
sum of i where i =1, n+1 is (n+1)(n+2) / 2
pull n+1 out of the sum and we get
sum of i where i =1, n+1 is n+1 + sum of i where i =1,n is (n+1)+ n(n+1)/2
factor out (n+1) and simplify
(n+1) + n(n+1) / 2 = (n+1)(1+ n/2) = (n+1)(2+n)/2 = (n+1)(n+2) / 2
which proves the result