Let P(n) be statement that 12 +22 + ... .+n2 = n(n+1)(2n +1)/6 for positive integer n.
i) Determine the statement P(1)?
ii) Illustrate that P(1) is true, completing basis step of proof.
iii) Determine inductive hypothesis?
iv) What do you require to prove in inductive step?
v) Complete inductive step, identifying where you use inductive hypothesis.
vi) Describe why the steps show that the formula is true whenever n is the positive integer.