/*! 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 73 What is the meaning of the symbo... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Problem 73

What is the meaning of the symbol \(\Sigma ?\) Give an example with your description.

Short Answer

Expert verified
The symbol \(\Sigma\) in mathematics represents 'sum'. It is used for expressing the sum of a series. For example, the sum of integers from 1 through 4 using \(\Sigma\) notation would be \(\Sigma_{i=1}^{4} i = 1 + 2 + 3 + 4 = 10\).

Step by step solution

01

Explanation of Symbol

In mathematics, the uppercase Sigma \(\Sigma\) is used to represent the 'sum' of a sequence or series. This sum is achieved by adding up all the terms present in the series.
02

Using Sigma Notation

When using \(\Sigma\), the general format is \(\Sigma_{i=a}^{b} f(i)\). Here, \(i\) is the index of summation; \(a\) and \(b\) are the lower and upper bounds of the sum, respectively; and \(f(i)\) is the function to be summed.
03

Examples

For example, in the expression \(\Sigma_{i=1}^{4} i\), sum all integer numbers from 1 (the bottom number, or \(a\)) through 4 (the top number, or \(b\)). The value of this expression is 1 + 2 + 3 + 4 = 10.

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!

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

How do you determine if an infinite geometric series has a sum? Explain how to find the sum of an infinite geometric series.

Use the Binomial Theorem to find a polynomial expansion for each function. Then use a graphing utility and an approach similar to the one in Exercises 64 and 65 to verify the expansion. $$ f_{1}(x)=(x+2)^{6} $$

Which one of the following is true? a. The sequence \(2,6,24,120, \ldots\) is an example of a geometric sequence. b. The sum of the geometric series \(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\dots+\frac{1}{512}\) can only be estimated without knowing precisely which terms occur between \(\frac{1}{8}\) and \(\frac{1}{512}\). c. \(10-5+\frac{5}{2}-\frac{5}{4}+\cdots=\frac{10}{1-\frac{1}{2}}\) d. If the \(n\) th term of a geometric sequence is \(a_{n}=3(0.5)^{n-1},\) the common ratio is \(\frac{1}{2}\).

Explain how to find the probability of an event not occurring. Give an example.

a. If two people are selected at random, the probability that they do not have the same birthday (day and month) is \(\frac{255}{365} \cdot \frac{364}{368} .\) Explain why this is so. (Ignore leap years and assume 365 days in a year.) b. If three people are selected at random, find the probability that they all have different birthdays. c. If three people are selected at random, find the probability that at least two of them have the same birthday. d. If 20 people are selected at random, find the probability that at least 2 of them have the same birthday. e. How large a group is needed to give a 0.5 chance of at least two people having the same birthday?
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Pure Maths

Read Explanation

Mechanics Maths

Read Explanation

Statistics

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.