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College Algebra
1st Edition
ISBN: 9781938168383
Author: Jay Abramson
Publisher: OpenStax
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Question
For the following, write its recursive definition:
![The image shows a mathematical expression related to products in sequences:
\[
\prod_{k=1}^{n} a_{k}, \text{ for } n \geq 1
\]
This expression represents the product of a sequence of terms \( a_k \), starting from \( k = 1 \) up to \( k = n \). The condition \( n \geq 1 \) indicates that the product is defined only for positive integer values of \( n \). Therefore, it calculates the multiplication of the terms \( a_1 \times a_2 \times \cdots \times a_n \). This notation is often used in mathematics to succinctly represent such multiplicative processes in sequences.](https://content.bartleby.com/qna-images/question/bfcb3af0-6e5c-49af-8aa4-5de9c395dfb0/ee67df0d-ecac-499e-8874-9236df574a9a/1iex21b_thumbnail.jpeg)
Transcribed Image Text:The image shows a mathematical expression related to products in sequences:
\[
\prod_{k=1}^{n} a_{k}, \text{ for } n \geq 1
\]
This expression represents the product of a sequence of terms \( a_k \), starting from \( k = 1 \) up to \( k = n \). The condition \( n \geq 1 \) indicates that the product is defined only for positive integer values of \( n \). Therefore, it calculates the multiplication of the terms \( a_1 \times a_2 \times \cdots \times a_n \). This notation is often used in mathematics to succinctly represent such multiplicative processes in sequences.
Expert Solution
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Step 1
Consider for .
A recursive definition is one which defines the elements of the sequence in terms of the previous terms.
When , we have
When , we have
Step by stepSolved in 2 steps
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