(1+1/2)x(1+1/3)x(1+1/4)x(1+1/120)

2 min read Jun 16, 2024
(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.

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