Let n0 Є N and let P (n) be a statement for each natural number n ≥ n0. Suppose that
- The statement P (n0) is true.
- For all n ≥ n0, P (K) is true => P (K + 1) is true.
Then P (n) is true for all n ≥ n0.
Cube: 1³ + 2³ + 3³ + … + n³ = \(\frac{{{n}^{2}}{{\left( n+1 \right)}^{2}}}{4}\), n ϵ N.
Sum of the ‘n’ numbers: 1 + 2 + 3 + … + n = \(\frac{n\left( n+1 \right)}{2}\).
Square: 1² + 2² + 3² + … + n² = \(\frac{n\left( n+1 \right)\left( 2n+1 \right)}{6}\).