Textbook Question
Sigma notation Evaluate the following expressions.
(b) 10
∑ (2κ + 1)
κ=1
Ch. 5 - Integration
Briggs3rd EditionCalculus: Early TranscendentalsISBN: 9780136847243
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Table of contents
- Ch. 1 - Functions210
- Ch. 2 - Limits371
- Ch. 3 - Derivatives633
- Ch. 4 - Applications of the Derivative412
- Ch. 5 - Integration328
- Ch. 6 - Applications of Integration331
- Ch. 7 - Logarithmic, Exponential Functions, and Hyperbolic Functions177
- Ch. 8 - Integration Techniques394
- Ch. 9 - Differential Equations179
- Ch. 10 - Sequences and Infinite Series339
- Ch. 11 - Power Series218
- Ch.12 - Parametric and Polar Curves215
Briggs3rd EditionCalculus: Early TranscendentalsISBN: 9780136847243Not the one you use?Change textbook
Chapter 5, Problem 5.1.47b
Sigma notation Express the following sums using sigma notation. (Answers are not unique.)
(b) 4 + 5 + 6 + 7 + 8 + 9
Verified step by step guidance1
Step 1: Understand the problem. The goal is to express the sum 4 + 5 + 6 + 7 + 8 + 9 using sigma notation, which is a compact way to represent summation.
Step 2: Identify the pattern in the sequence. The numbers in the sum are consecutive integers starting from 4 and ending at 9.
Step 3: Define the general term of the sequence. The general term can be written as , where represents each integer in the sequence.
Step 4: Determine the range of the index. The sequence starts at 4 and ends at 9, so the index will range from 4 to 9.
Step 5: Write the sum in sigma notation. The sum can be expressed as .
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Sigma Notation
Sigma notation is a concise way to represent the sum of a sequence of numbers. It uses the Greek letter sigma (Σ) to indicate summation, followed by an expression that defines the terms to be added. The notation typically includes an index of summation, which specifies the starting and ending values for the variable that represents the terms in the sum.
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Sigma Notation
Index of Summation
The index of summation is a variable used in sigma notation to denote the position of each term in the sequence being summed. It usually starts at a specified lower limit and increments by one until it reaches an upper limit. For example, in the sum Σ from i=1 to n, 'i' is the index that takes on integer values from 1 to n, allowing for the systematic addition of terms.
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Arithmetic Sequence
An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. In the case of the sum 4 + 5 + 6 + 7 + 8 + 9, the common difference is 1. Recognizing that the terms form an arithmetic sequence helps in expressing the sum using sigma notation, as it allows for a general formula to represent the terms based on their position in the sequence.
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5:17Arithmetic Sequences - General Formula
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