(Choose 1 answer)
(See picture)
A. (iii)
B. (ii)
C. None of the other choices is correct
D. (i)
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.
For a proof by mathematical induction, assume that P(k) is true for some integer k\ge0 What do you need to prove in the inductive step?
(i)1^{2}+3^{2}+5^{2}+\cdot\cdot\cdot+(2k+1)^{2}=\frac{(k+1)(2k+1)(2k+3)}{3}
14/50-CAP
(ii)1^{2}+3^{2}+5^{2}+\cdot\cdot\cdot+(2k-1)^{2}=\frac{k(2k-1)(2n+1)}{3}
Giii)1^{2}\perp2^{2}\perp5^{2}\perp...\perp(2b\perp2)^{2}-\frac{(k+2)(2k+3)(2k+5)}
R
Q: 16
