The Nth triangle number is given by N(N+1)/2.
The first number is 1.
The first difference is 2.
The second differences are all 1.
The polynomial describing this series can be written as
1 + (n-1)/1(2 + (n-2)/2(1))
= 1 + (n-1)((4 + n - 2)/2)
= 1 + (n-1)(n+2)/2
= (2 + n^2 - n + 2n - 2)/2
= (n^2 + n)/2
= n(n+1)/2
The first number is 1.
The first difference is 2.
The second differences are all 1.
The polynomial describing this series can be written as
1 + (n-1)/1(2 + (n-2)/2(1))
= 1 + (n-1)((4 + n - 2)/2)
= 1 + (n-1)(n+2)/2
= (2 + n^2 - n + 2n - 2)/2
= (n^2 + n)/2
= n(n+1)/2
