x(1-1%2F3)x(1-1%2F4)x(1-1%2F5)x(1-1%2F6).jpeg "(1-1/2)x(1-1/3)x(1-1/4)x(1-1/5)x(1-1/6)")
The Mysterious Product: (1-1/2)x(1-1/3)x(1-1/4)x(1-1/5)x(1-1/6)
Have you ever wondered what happens when you multiply a series of fractions together? In this article, we'll explore the fascinating result of multiplying the fractions (1-1/2), (1-1/3), (1-1/4), (1-1/5), and (1-1/6).
Breaking Down the Problem
Let's start by evaluating each fraction individually:
(1-1/2) = 1/2(1-1/3) = 2/3(1-1/4) = 3/4(1-1/5) = 4/5(1-1/6) = 5/6
Now, let's multiply these fractions together:
The Calculation
(1/2) × (2/3) × (3/4) × (4/5) × (5/6) = ?
To multiply these fractions, we need to multiply the numerators (the numbers on top) and multiply the denominators (the numbers on the bottom), like this:
(1 × 2 × 3 × 4 × 5) / (2 × 3 × 4 × 5 × 6) = ?
The Result
After multiplying the numerators and denominators, we get:
120 / 720 = 1/6
The final answer is 1/6!
Conclusion
The product of (1-1/2)x(1-1/3)x(1-1/4)x(1-1/5)x(1-1/6) is surprisingly simple: 1/6. This result may seem unexpected, but it demonstrates the beauty of mathematical patterns and the importance of breaking down complex problems into manageable parts.
