Son conocidas las relaciones $$\eqalign { \sum_{k=1}^n k &= \frac{1}{2} n(n+1) &= \frac{1}{2} n^2 + \frac{1}{2} n \\ \sum_{k=1}^n k^2 &= \frac{1}{6} n(n+1)(2n+1) &= \frac{1}{3} n^3 + \frac{1}{2} n^2 + \frac{1}{6} n \\ \sum_{k=1}^n k^3 &= \frac{1}{4} n^2 (n+1)^2 &= \frac{1}{4} n^4 + \frac{1}{2} n^3 + \frac{1}{4} n^2 }$$ En ocasiones se pide demostrar su...