Let be a positive integer. We will write the sum of the first integers.
1)
So if we sum these two equations, we get
, that is to say
Therefore
2)
What are the first odd integers?
So their sum is
3)
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