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RESUMEN En este manuscrito, se demuestra que la potencia de (p + q) a cualquier potencia (n), siendo n un numero natural puede expresarse como la suma de una serie de impares consecutivos. Variando los indices de los numeros impares entre un limite inferior que es la mitad de la diferencia entre la potencias p y q del natural n mas 1, y el limite superior, la mitad de esas potencias. El algoritmo recalcando su simplicidad, ofrece una oportunidad interesante en las aplicaciones de teorias de numeros a analisis numerico. Palabras clave: Numero natural, impares, sumatoria, formula de potencia. ABSTRACT In this paper it is demonstrated that the power (p + q) of a natural number (n), can be derived as the sum of a series of consecutive odd numbers. The series of the summation is conditioned by a lower and upper boundary, being equal to half the difference plus 1, and respectively half the sum of the powers p and q of the natural number. The algorithm, notwithstanding its simplicity, offers some interesting opportunities in the applications of number theory to numerical analysis. Keywords: Natural number, odd, sum, power formula.

Potencias de números enteros como suma de impares consecutivos