4 Compute the product II (-2) j=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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Question
![**Instructions: Compute the Product**
Evaluate the product given by:
\[
\prod_{j=0}^{4} (-2)^j
\]
### Explanation:
This expression involves finding the product of the terms \((-2)^j\) for \(j\) ranging from 0 to 4.
### Steps to Compute:
1. **Substitute each value of \(j\):**
- For \(j = 0\): \((-2)^0 = 1\)
- For \(j = 1\): \((-2)^1 = -2\)
- For \(j = 2\): \((-2)^2 = 4\)
- For \(j = 3\): \((-2)^3 = -8\)
- For \(j = 4\): \((-2)^4 = 16\)
2. **Product Calculation:**
Multiply all the results together:
\[
1 \times (-2) \times 4 \times (-8) \times 16
\]
3. **Step-by-Step Computation:**
- \(1 \times (-2) = -2\)
- \(-2 \times 4 = -8\)
- \(-8 \times (-8) = 64\)
- \(64 \times 16 = 1024\)
4. **Conclusion:**
Therefore, the product is \(1024\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb34753c0-065a-4307-ab8c-7afc3888779e%2Fdda74d2b-353a-422f-92ea-63c491d5ffa6%2Fzj5lrg_processed.png&w=3840&q=75)
Transcribed Image Text:**Instructions: Compute the Product**
Evaluate the product given by:
\[
\prod_{j=0}^{4} (-2)^j
\]
### Explanation:
This expression involves finding the product of the terms \((-2)^j\) for \(j\) ranging from 0 to 4.
### Steps to Compute:
1. **Substitute each value of \(j\):**
- For \(j = 0\): \((-2)^0 = 1\)
- For \(j = 1\): \((-2)^1 = -2\)
- For \(j = 2\): \((-2)^2 = 4\)
- For \(j = 3\): \((-2)^3 = -8\)
- For \(j = 4\): \((-2)^4 = 16\)
2. **Product Calculation:**
Multiply all the results together:
\[
1 \times (-2) \times 4 \times (-8) \times 16
\]
3. **Step-by-Step Computation:**
- \(1 \times (-2) = -2\)
- \(-2 \times 4 = -8\)
- \(-8 \times (-8) = 64\)
- \(64 \times 16 = 1024\)
4. **Conclusion:**
Therefore, the product is \(1024\).
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