Estimated Sums in Infinite Series Problem

Thread starter pjcircle
Start date Jan 30, 2013
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Infinite Infinite series Series Sums

In summary, an estimated sum in an infinite series problem is the sum of an infinite number of terms in a sequence that is approximated or calculated through a specific method or formula. There are various methods to find the estimated sum, including the geometric series formula, the telescoping series method, and the integral test. The purpose of estimating sums in infinite series problems is to calculate infinite quantities that cannot be solved by traditional methods and understand the behavior and patterns of infinite sequences and series. Some common types of infinite series problems that require estimating sums include geometric series, harmonic series, alternating series, and power series. However, an estimated sum in an infinite series problem is not exact and becomes more accurate as the number of terms used in the calculation increases.

Jan 30, 2013

pjcircle

Homework Statement

How many terms of the series do we need to add in order to find the sum to the indicated accuracy?
Ʃ((-1)ⁿ)/(n(10ⁿ)) from n=1 to infinity
|error| <.0001

I keep ending up with n=log(4)-log(n)

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Jan 30, 2013

haruspex

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1. What is an estimated sum in an infinite series problem?

An estimated sum in an infinite series problem is the sum of an infinite number of terms in a sequence that is approximated or calculated through a specific method or formula. It is used in mathematics and physics to solve problems that involve infinite quantities.

2. How do you find the estimated sum in an infinite series problem?

There are various methods to find the estimated sum in an infinite series problem, including the geometric series formula, the telescoping series method, and the integral test. The specific method used will depend on the type of series and the information given in the problem.

3. What is the purpose of estimating sums in infinite series problems?

Estimating sums in infinite series problems is essential because it allows us to calculate infinite quantities that cannot be solved by traditional methods. It also helps us understand the behavior and patterns of infinite sequences and series.

4. What are some common types of infinite series problems that require estimating sums?

Some common types of infinite series problems that require estimating sums include geometric series, harmonic series, alternating series, and power series. These types of series appear in various mathematical and scientific contexts, such as calculus, physics, and finance.

5. Can an estimated sum in an infinite series problem be exact?

No, an estimated sum in an infinite series problem is not exact. It is an approximation that becomes more accurate as the number of terms used in the calculation increases. To get an exact sum, an infinite number of terms would need to be added, which is not possible in most cases.