Proof by induction that $1^2 + 2^2 + \dots + n^2 = \frac{n(n+1)(2n+1)}{6}$

Question

How would I go about solving this question?

Use induction to prove that for all integers $n ≥ 1$, $$1^2 + 2^2 + 3^2 + \dots + n^2 = \frac{n(n+1)(2n+1)}{6}$$

Answer 1

Hint:

1. Prove it is true for $n=1$

2. Assume it is true for $n=k$ and show it is true for $n=k+1$, for example by adding $(k+1)^2$ to both sides of $\displaystyle\sum_{i=1}^k i^2 = k(k+1)(2k+1)/6$ and then simplyfying the right hand side

3. Claim this proves the hypothesis for all $n \ge 1$, by induction