Sum of Arithmetic Series
Suppose S=SUM(1 to n) a+bn
S=n(a + b(n+1)/2)
Proof:
Basis for induction:
n=1 => S=a+b
Inductive hypothesis:
SUM(1 to n+1) a+bn=SUM(1 to n) a+bn +a+b(n+1)
=n(a + b(n+1)/2) + a+b(n+1)
=(n+1)(a + b(n/2 + 1))
=(n+1)(a + b((n+2)/2))