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Propiedades de la Sumatoria - Problemas y ejercicios de matematica

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Propiedades de Sumatoria

 

 

 

 

 

Las propiedades de la sumatoria permiten realizar cálculos, en muchos casos la sumatoria se asocia con problemas de Inducción completa, pero en realidad existe por sí misma. Las series de números son una aplicación importante de la sumatoria, el estudio de seres matemáticas lleva a un tratamiento complejo del tema.

 

Las propiedades no serán demostradas en este caso para evitar largos desarrollos, si Uds desean demostraciones pueden solicitarlas en el foro que con gusto las dejaremos.

 

 

 

 

El desarrollo de una sumatoria consiste en usar el término general sustituyendo la variable por el índice correspondiente, y luego calcular el resultado, va un ejemplo

    desarrollamos

 



 

 

 

 

 

 

 

 

Propiedades Generales

 

 

 

1)  

 

 

 

2)   

 

 

 

3)    siendo a un número

 

 

 

4) Sumas parciales

 

 

 

5)

 

 

 

Es un buen ejercicio para el que lo desee, demostrar estas propiedades en base a las propiedades conocidas de la suma,de hecho estas propiedades se dejan como ejercicios en la sección correspondiente

Existen mas propiedades de la sumatoria, sobre todo las que se desprenden de los posibles despejes que se pueden realizar en la última fórmula, en realidad la misma se utiliza para detallar que cualquier suma puede ser separada en la cantidad de sumas parciales que se necesiten, respetando los índices.

Additional information