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Electrical Engineering

What will be the sum of the following series: x(n)=1+(1/3)+(1/9/+(1/27)+.... To infinity

Delmar's Standard Textbook Of Electricity

7th Edition

ISBN:9781337900348

Author:Stephen L. Herman

Publisher:Stephen L. Herman

Chapter16: Inductance In Ac Circuits

Section: Chapter Questions

Problem 1PP: Inductive Circuits Fill in all the missing values. Refer to the following formulas:...

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Concept explainers

Capacitor

The capacitor is an element used to store electrical energy in the electrical field. A capacitor is a form of passive energy.

Question

What will be the sum of the following series:

x(n)=1+(1/3)+(1/9/+(1/27)+.... To infinity

Expert Solution

Step 1

The given series form a geometric progression (GP). The initial term and the common ratio of the series can be expressed as

$a = 1 r = \frac{\frac{1}{3}}{1} = \frac{1}{3}$

The sum of an infinite GP series can be expressed as

$S = \frac{a}{1 - r}$

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