The sum of the first n positive perfect squares, where n is a positive integer, is given by the formula n^3/3 + c*n^2 + n/6, where c is a constant. What is the sum of the first 18 positive perfect squares?  Choices:  A) 1,010  B) 1,164  C) 1,240  D) 1,316  E) 2,109
First we need to find the constant 'c'. The easiest way to find this is for the sum of the first two perfect squares for 1 and 2 = 1 and 4 respectively.   Hence LHS = 1+4 and plug n=2 for RHS and simplify to get c = 1/2.   Plug values of n = 18 and c = 1/2 into the equation and simplify to get the answer 2109.   Option 2,109.
<result>E</result>
The sum of the first n positive perfect squares, where n is a positive integer, is given by the formula n^3/3 + c*n^2 + n/6, where c is a constant. What is the sum of the first 18 positive perfect squares?