Calculate the following II i =1 2.
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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![**Calculate the following:**
\[
\prod_{i=1}^{2} \binom{3}{i}
\]
**Explanation:**
The expression involves calculating a product of binomial coefficients from \(i = 1\) to \(i = 2\).
### Step-by-Step Calculation:
1. **Determine each binomial coefficient:**
- For \( i = 1 \): \(\binom{3}{1}\)
- For \( i = 2 \): \(\binom{3}{2}\)
2. **Calculate each coefficient:**
- \(\binom{3}{1} = 3\)
- \(\binom{3}{2} = 3\)
3. **Calculate the product:**
- \(\prod_{i=1}^{2} \binom{3}{i} = 3 \times 3 = 9\)
Thus, the result of the expression is \(9\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F73f22fda-350d-4c0b-9260-2b8a3ecf6175%2F507ac224-d444-4532-b148-61cc78b39d67%2Fxgev8h_processed.png&w=3840&q=75)
Transcribed Image Text:**Calculate the following:**
\[
\prod_{i=1}^{2} \binom{3}{i}
\]
**Explanation:**
The expression involves calculating a product of binomial coefficients from \(i = 1\) to \(i = 2\).
### Step-by-Step Calculation:
1. **Determine each binomial coefficient:**
- For \( i = 1 \): \(\binom{3}{1}\)
- For \( i = 2 \): \(\binom{3}{2}\)
2. **Calculate each coefficient:**
- \(\binom{3}{1} = 3\)
- \(\binom{3}{2} = 3\)
3. **Calculate the product:**
- \(\prod_{i=1}^{2} \binom{3}{i} = 3 \times 3 = 9\)
Thus, the result of the expression is \(9\).
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