Answer
$\frac{(k + 1)((k + 1) + 1)(2(k + 1) + 1)}{6}$
Work Step by Step
In the inductive step, both the inductive hypothesis and what is to be shown are wrong.
The inductive hypothesis should be Suppose that for some integer k ≥ 1,
12 + 22 +· · ·+$k^2$ = $\frac{k(k + 1)(2k + 1)
}{6}$
.
And what is to be shown should be
12 + 22 +· · ·+$(k + 1)^2$=$\frac{(k + 1)((k + 1) + 1)(2(k + 1) + 1)}{6}$
