1 1 3i +1 3i+2 3i + 3) 1 1 Problem 2: Prove that Vn e Z such that n >0,I (Зп + 3)! i=0
1 1 3i +1 3i+2 3i + 3) 1 1 Problem 2: Prove that Vn e Z such that n >0,I (Зп + 3)! i=0
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Problem 2: Prove that for all \( n \in \mathbb{Z} \) such that \( n \geq 0 \),**
\[
\prod_{i=0}^{n} \left( \frac{1}{3i+1} \cdot \frac{1}{3i+2} \cdot \frac{1}{3i+3} \right) = \frac{1}{(3n+3)!}.
\]
If correct, then fill in the needed to:
- Make the proof completely correct.
- Make sure each assertion made is fully justified.
- Make the proof written in such a way that a student in the class could follow the logic and be fully convinced that the theorem is true.
If incorrect, then:
- Identify any errors in the proof above.
- Explain each error. Your explanation should be written to the student who made the error, and should try to help the student understand why what they wrote is incorrect.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F650a3720-d25f-4113-9d71-11ba929e1f84%2F61ac7043-9226-42dd-87ca-f4563345464c%2F74g5slq_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 2: Prove that for all \( n \in \mathbb{Z} \) such that \( n \geq 0 \),**
\[
\prod_{i=0}^{n} \left( \frac{1}{3i+1} \cdot \frac{1}{3i+2} \cdot \frac{1}{3i+3} \right) = \frac{1}{(3n+3)!}.
\]
If correct, then fill in the needed to:
- Make the proof completely correct.
- Make sure each assertion made is fully justified.
- Make the proof written in such a way that a student in the class could follow the logic and be fully convinced that the theorem is true.
If incorrect, then:
- Identify any errors in the proof above.
- Explain each error. Your explanation should be written to the student who made the error, and should try to help the student understand why what they wrote is incorrect.
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