2)Define the sequence: a, = (n+1)! (n = 1,2,3, ...) recursively. %3D

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question
The task is to define the sequence \( a_n = (n+1)! \) where \( n = 1, 2, 3, \ldots \) recursively. 

In mathematical terms, a recursive definition provides a way to determine each term of the sequence based on the preceding terms. For this sequence:

- Base Case: Start with an initial value. For example, \( a_1 \) can be initially defined as \( 2! = 2 \).
- Recursive Step: For \( n \geq 1 \), define \( a_{n} = (n+1) \times a_{n-1} \).

This means that each term in the sequence is determined by multiplying the previous term by \( n+1 \). Thus, the sequence builds factorials successively starting from \( 2! \).
Transcribed Image Text:The task is to define the sequence \( a_n = (n+1)! \) where \( n = 1, 2, 3, \ldots \) recursively. In mathematical terms, a recursive definition provides a way to determine each term of the sequence based on the preceding terms. For this sequence: - Base Case: Start with an initial value. For example, \( a_1 \) can be initially defined as \( 2! = 2 \). - Recursive Step: For \( n \geq 1 \), define \( a_{n} = (n+1) \times a_{n-1} \). This means that each term in the sequence is determined by multiplying the previous term by \( n+1 \). Thus, the sequence builds factorials successively starting from \( 2! \).
Expert Solution
steps

Step by step

Solved in 2 steps with 1 images

Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,