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Programa resuelto con recursividad
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Programa que plantea la resolución de un problema con recursividad. Muestra el código y la explicación paso a paso del mismo
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Problema:13. Dada la siguiente serie an=an-1+2n, para n > 0 (para n=0, an=0), diseñar una función recursiva que
calcule el término n de la serie.
Solución:
Crear un programa recursivo que nos pida el término “n” a buscar, el cual es el siguiente:
public class Calcular_n {
public static void main(String[] args) {
// Alrak Studios (2023)
int n;
Scanner scanner = new Scanner(System.in);
System.out.println("Ingrese el término a buscar:");
n = scanner.nextInt();
int r=CS(n);
System.out.println("El termino " + n + " de la serie es: " + r);
}
public static int CS(int n) {
if (n==0) {
return 0;
}else {
int an= CS(n-1);
return (an-1)+2*n;
} //Formula: an = an-1 + 2n
}
Interpretación del programa:
Lo que hace el programa es pedir al usuario el término “n” a buscar. En nuestro caso base tenemos:
if (n==0) {return 0;}
Lo cual significa que si “n” o “an” es igual a 0, entonces nuestro programa terminará.
En caso de nuestra parte recursiva tenemos:
else {
int an= CS(n-1);
return (an-1)+2*n;
}
El cuál crea la variable “an” para guardar la posición en la que se encuentra y sucesivamente realizar la
operación de la fórmula an-1+2n.
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