Question: 53
(Choose 1 answer)
(See picture)
A. (i)
B. (ii)
C. (iii)
D. (iv)
In the inductive proof of the proposition
1^{2}+2^{2}+...+n^{2}=n(n+1)(2n+1)/6~for~all~n\ge1",
which of the following equations is used?
(i) l^{2}+2^{2}+...+(k+1)^{2}=k(k+1)(2k+1)/6+k^{2}+1
(ii) 2+2^{2}+...+(k+1)^{2}=k(k+1)(2k+1)/6+(2k+1)
(iii) 1^{2}+2^{2}+...+(k+1)^{2}=k(k+1)(2k+1)/6+(k+1)^{2}
(iv) 1^{2}+2^{2}+...+(k+1)^{2}=k(k+1)(2k+1)/6+k^{2}
