Question

Evaluate each series. \sum_{i=1}^{4}(5-2 i)

   Evaluate each series.
\sum_{i=1}^{4}(5-2 i)

Beginning and Intermediate Algebra

Beginning and Intermediate Algebra

Sherri Messersmith 2nd Edition

Chapter 15, Problem 42

Instant Answer

Solved by Expert Amy Jiang

06/26/2020

Step 1

The series is given by \(\sum_{i=1}^{4}(5-2 i)\). This means we need to substitute \(i = 1, 2, 3, 4\) into the expression \(5-2i\) and add the results. Show more…

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Evaluate each series. \sum_{i=1}^{4}(5-2 i)

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Key Concepts

Summation Notation

Summation notation is a concise way to represent the addition of a sequence of terms. It uses the sigma symbol (?) to denote the sum, with an index that runs over a specified set of values. This notation helps in expressing long sums in a compact form and is a fundamental tool in mathematics for dealing with series.

Finite Series

A finite series is the sum of a sequence of terms that has a definite number of terms. Evaluating a finite series typically involves substituting each index value into the given expression and adding all the resulting numbers. Understanding finite series is crucial for solving problems in algebra and calculus where the number of terms is fixed.

Index Substitution

Index substitution involves replacing the index variable in a summation with its successive integer values, which is essential for finding the individual terms of the series. This method is used to break down the summation into a series of operations, enabling step-by-step evaluation and analysis of the sum.

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