x(1%2B1%2F3)x(1%2B1%2F4)x(1%2B1%2F120).jpeg "(1+1/2)x(1+1/3)x(1+1/4)x(1+1/120)")
Unraveling the Mystery: (1+1/2)x(1+1/3)x(1+1/4)x(1+1/120)
This seemingly complex expression might seem daunting at first glance, but with a bit of mathematical insight, we can easily break it down and find its solution.
Simplifying the Expression
The key to solving this lies in recognizing a pattern within the brackets. Notice how each term is in the form of (1 + 1/n). Let's simplify each term:
- (1 + 1/2) = 3/2
- (1 + 1/3) = 4/3
- (1 + 1/4) = 5/4
- (1 + 1/120) = 121/120
Now, our expression becomes: (3/2) x (4/3) x (5/4) x (121/120)
Cancelling Out Common Factors
Notice that there are common factors that can be canceled out in this multiplication:
- 3 cancels with 3
- 4 cancels with 4
This leaves us with: (3/2) x (5/1) x (121/120)
Final Calculation
Now we can easily multiply the remaining terms:
(3 x 5 x 121) / (2 x 1 x 120) = 1815 / 240 = 7.5625
Therefore, the solution to the expression (1+1/2)x(1+1/3)x(1+1/4)x(1+1/120) is 7.5625.
This problem illustrates how a seemingly complex mathematical expression can be simplified by recognizing patterns and employing basic mathematical principles like cancellation.