Let be a positive integer. We will write the sum of the first integers.
So if we sum these two equations, we get
, that is to say
What are the first odd integers?
So their sum is
It's easier than 2)
1. Find the equation that gives the sum of the first n positive integer
the answer given was n(n+1)/2 - but I don't know how to get it
2. Show that the sum of the first n odd integers is equal to the perfect square n^2
3. Show that the sum of the first n even integers is equal to n^2 + n