Problem: 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 ?
Rationale: 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 e .
annotated_formula: divide(divide(multiply(multiply(18, add(18, const_1)), add(multiply(18, const_2), const_1)), 6), divide(multiply(multiply(18, add(18, const_1)), add(multiply(18, const_2), const_1)), 6))