Problem: The sum of the squares of the first n positive integers is given by the expression 6n(n+c)(2n+k)​, if c and k are, respectively:
Answer Choices:
A. 1 and 2
B. 3 and 5
C. 2 and 2
D. 1 and 1
E. 2 and 1
Solution:
The formula is S=n(n+1)(2n+1)/6;
or
first let S=12 and then let S=12+22.
12=61(1+c)(2+k)​
and
12+22=62(2+c)(4+k)​.
Solving for c and k, we have c=k=1.