For the following, write its recursive definition:

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
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ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:HOUGHTON MIFFLIN HARCOURT
Chapter6: Exponential Functions And Sequences
Section: Chapter Questions
Problem 9CT
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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.
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
Step 1

Consider k=1nak for n1.

A recursive definition is one which defines the elements of the sequence in terms of the previous terms.

When n=1, we have 

k=1nak=k=11ak=a1

When n=2, we have 

k=1nak=k=12ak=a1a2

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