Explanation Consider the given expression 2 k − 1 3 k + 1 = 3 k − k − 1 3 k + 1 = 3 k − ( k + 1 ) 3 k + 1 = k 3 k − ( k + 1 ) 3 k + 1 The sum of the given series ∑ k = 1 ∞ 2 k − 1 3 k + 1 can thus be calculated as shown: ∑ a k = ∑ k = 1 ∞ 2 k − 1 3 k + 1 = ∑ k = 1 ∞ k 3 k − ( k + 1 ) 3 k + 1 S n = ∑ k = 1 n [ k 3 k − ( k + 1 ) 3 k + 1 ] = ( ( 1 3 1 − 2 3 2 ) + ( 2 3 2 − 3 3 3 ) + ( 3 3 3 − 4 3 4 ) + ..

Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)

6th Edition

ISBN: 9781524908102

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Addition Rule of Probability

It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.

Expected Value

When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known …

Probability Distributions

Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosi…

Basic Probability

The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the prob…

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Chapter 8.2, Problem 36PS

To determine

To find: the sum of the series: ∑k=1∞2k−13 k+1

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Chapter 8.2, Problem 35PS

Chapter 8.2, Problem 37PS

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Chapter 8 Solutions

Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)

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the sum of the series: ∑ k = 1 ∞ 2 k − 1 3 k + 1

Solution Summary: The author explains how the sum of the given series is 1.

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Chapter 8 Solutions