/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 67 Use the summation properties and... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 11: Problem 67

Use the summation properties and rules to evaluate each series. $$\sum_{i=1}^{100} 6$$

Short Answer

Expert verified
600

Step by step solution

01

Identify the Series

The given series is \(\backslash \sum_{i=1}^{100} 6\). It is a sum of constant terms.
02

Apply Summation Rule for Constants

The summation rule for a constant term is \(\backslash \sum_{i=1}^{n} c = c \times n\), where \(c\) is the constant term, and \(n\) is the number of terms.
03

Calculate the Result

Here, \backslash( c = 6\) and \(n = 100 \backslash). Using the rule, \(\backslash \sum_{i=1}^{100} 6 = 6 \times 100 = 600\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

series evaluation
When asked to evaluate a series, the goal is to find the sum of all its terms.
Understanding how to approach series evaluation can simplify many mathematical problems involving sums.
Let's break it down with an example where there is a constant term added multiple times.
In our exercise, we need to evaluate the series \(\sum_{i=1}^{100} 6\).
This means adding the number 6 exactly 100 times.
With some simple steps, the series evaluation becomes much easier. Determining the nature of the series is our first step.
summation rule for constants
One of the most useful rules when dealing with series is the summation rule for constants. This rule states that for a constant term c, the summation for n terms is simply the constant multiplied by the number of terms:
\[\sum_{i=1}^{n} c = c \times n\]\
In our given exercise, the constant is 6, and there are 100 terms.
Applying the rule, we get:\
\[\sum_{i=1}^{100} 6 = 6 \times 100\]\
The rule makes it incredibly efficient to solve such problems without having to manually add each term.
All we need to do is identify the constant and the number of terms, and then multiply them.
constant term summation
Summing constant terms is a particular case in evaluating series.
It highlights the usefulness of the summation rule for constants.
In our example, the term 6 is counted 100 times. This means we effectively multiply 6 by 100, which simplifies the calculation to:\
\[6 \times 100 = 600\]\
Constant term summation is straightforward but fundamental.
It paves the way for understanding more complex series evaluations.
Remember, recognizing the type of series and applying the correct rule is crucial in mathematics.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Find all natural number values for \(n\) for which the given statement is false. $$2^{n}>n^{2}$$

If your college offers 400 courses, 20 of which are in mathematics, and your counselor arranges your schedule of 4 courses by random selection, how many schedules are possible that do not include a math course?

Use summation notation to write each series. $$\frac{1}{3(1)}+\frac{1}{3(2)}+\frac{1}{3(3)}+\dots+\frac{1}{3(9)}$$

Use the summation properties and rules to evaluate each series. $$\sum_{i=1}^{6}\left(2+i-i^{2}\right)$$

Find all natural number values for \(n\) for which the given statement is false. $$2^{n}>2 n$$
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Logic and Functions

Read Explanation

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Calculus

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.