Question: 51
(Choose 1 answer)
(See picture)
A. (i)
B. (ii)
C. (iii)
D. (iv)
Let P(n) be the statement that 1^{2}+3^{2}+5^{2}+\cdot\cdot\cdot+(2n+1)^{2}=\frac{(n+1)(2n+1)(2n+3)}{3} for the nonnegative integer n.
What is the inductive hypothesis in a proof by mathematical induction?
(i) P(k) is true for some integer k>0.
(ii) P(k) is true for some integer k\ge0.
(iii) P(k+1) is true for some integer k>0 .
(iv) P(k+1) is true for some integer k\ge0.
