/*! 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 47 Express each sum using summation... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Problem 47

Express each sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. $$1+2+3+\dots+30$$

Short Answer

Expert verified
The sum \(1+2+3+\ldots+30\) can be expressed in summation notation as \(\Sigma_{{i=1}}^{30} i\).

Step by step solution

01

Identify the series type and pattern

The given series is a list of consecutive natural numbers from 1 to 30. The series follows an arithmetic pattern where each succeeding number is increased by 1.
02

Define the General Form of Series

In an arithmetic series, each term can be defined by a formula. Since this series starts at 1 and increments by 1, we can say the ith term, denoted by \(a_i\), is exactly \(i\). So we can express any term in the series as \(a_i = i\).
03

Translating to Summation Notation

Sigma notation, also known as summation notation, consists of three parts. It has an uppercase sigma (\(\Sigma\)), a number at the bottom called the lower limit of summation (in this case, 1), and a number at the top called the upper limit of summation (in this case, 30). In the middle, we place the general form of the series \(a_i = i\). Putting all this together we write the series in the summation notation as \(\Sigma_{{i=1}}^{30} i\)

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

Describe the pattern on the exponents on \(b\) in the expansion of \((a+b)^{n}\).

Use the Binomial Theorem to expand each binomial and express the result in simplified form. $$ (3 x+y)^{3} $$

Give an example of two events that are not mutually exclusive.

Use the Binomial Theorem to expand each binomial and express the result in simplified form. $$ (3 x+1)^{4} $$

Explain how to find or probabilities with mutually exclusive events. Give an example.
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation

Calculus

Read Explanation

Pure Maths

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.