Question

Evaluate each series. $$\sum_{r=1}^{4} \frac{1}{j}$$

   Evaluate each series.
$$\sum_{r=1}^{4} \frac{1}{j}$$

Precalculus

Margaret L. Lial,… 4th Edition

Chapter 11, Problem 31

Instant Answer

Solved by Expert Anas Venkitta

03/17/2021

Step 1

Here, we have to find the sum of the sequence with the general term $\frac{1}{j}$, where $j$ starts from 1 and goes until 4. Show more…

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Evaluate each series. $$\sum_{r=1}^{4} \frac{1}{j}$$

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Key Concepts

Summation Notation

Summation notation is a concise way to represent the sum of a sequence of terms. The sigma (?) symbol is used along with an index variable that defines the starting and ending values for the sum. This notation simplifies the expression and manipulation of series in mathematical problems.

Index of Summation

The index of summation, often represented as a variable like r, serves as a dummy variable that iterates over the prescribed range in the series. It is essential to understanding how each term in the series is generated and ensures clarity when evaluating sums, especially when the terms are defined independently of the index.

Series

A series is the sum of the terms of a sequence. In the context of finite series, the sum is taken over a fixed number of terms, which allows for direct computation by adding each term. This concept is fundamental to many areas of mathematics, including algebra and calculus.

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