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4 Compute the product II (-2) j=0

4 Compute the product II (-2) j=0

Advanced Engineering Mathematics
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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**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 \(1024\).
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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