In Exercises 7 -12, use sigma notation to write the sum. [5((1)/(8))+3]+[5((2)/(8))+3]+⋯+[5((8)/

Name: Problem 9, Chapter 4: Essential Calculus
Uploaded: 2022-04-05T19:22:00-08:00
Duration: 2 min 26 s
Channel: Israel Hernandez
Description: In Exercises 7 -12, use sigma notation to write the sum. [5((1)/(8))+3]+[5((2)/(8))+3]+⋯+[5((8)/(8))+3]

step 1 In this problem, we are giving the following sum of terms. First, we have 5 times 1 over 8 plus

Question

In Exercises 7 -12, use sigma notation to write the sum. $$ \left[5\left(\frac{1}{8}\right)+3\right]+\left[5\left(\frac{2}{8}\right)+3\right]+\cdots+\left[5\left(\frac{8}{8}\right)+3\right] $$

   In Exercises 7 -12, use sigma notation to write the sum.
$$
\left[5\left(\frac{1}{8}\right)+3\right]+\left[5\left(\frac{2}{8}\right)+3\right]+\cdots+\left[5\left(\frac{8}{8}\right)+3\right]
$$

Essential Calculus

Ron Larson, Robert… 1st Edition

Chapter 4, Problem 9

Instant Answer

Solved by Expert Israel Hernandez

04/05/2022

Step 1

We can see that each term in the sum is of the form $5\left(\frac{n}{8}\right)+3$, where $n$ is the term number starting from 1. Show more…

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In Exercises 7 -12, use sigma notation to write the sum. $$ \left[5\left(\frac{1}{8}\right)+3\right]+\left[5\left(\frac{2}{8}\right)+3\right]+\cdots+\left[5\left(\frac{8}{8}\right)+3\right] $$

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Key Concepts

Sigma Notation

Sigma notation is a concise way to represent the sum of a sequence of terms. It uses the Greek letter ? to denote summation, which allows you to specify an expression to be summed along with a starting and ending index, making it easier to work with long or complex sums.

Index Variable

The index variable in sigma notation acts as a placeholder that represents each successive value in the given range. This variable is used within the general term of the expression being summed, and its value changes from the lower bound to the upper bound of the summation.

General Term Representation

The general term is the expression inside the sigma notation that represents any term in the series as a function of the index variable. Recognizing the pattern in the series allows you to express each term as a function of this index, which is then summed over the specified interval.

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