## Links forward

### Use of induction

Some series are easy to sum by spotting patterns. For example, we have seen that the sum of the first \(n\) odd numbers is

\[ 1 + 3 + 5 + \dots + (2n-1) = n^2. \]On the other hand, the formula for the sum of the first \(n\) squares,

\[ 1^2 + 2^2 + 3^2 + \dots + n^2 = \dfrac{1}{6}n(n+1)(2n+1), \]is hardly obvious and requires a proof. While the Greeks had some very creative proofs of results such as this, the best approach is to give a proof using mathematical induction.