(1-1/2)x(1-1/3)x(1-1/4)x(1-1/5)x(1-1/6)x(1-1/7)x(1-1/8)

2 min read Jun 16, 2024
(1-1/2)x(1-1/3)x(1-1/4)x(1-1/5)x(1-1/6)x(1-1/7)x(1-1/8)

Simplifying the Expression: (1-1/2)x(1-1/3)x(1-1/4)x(1-1/5)x(1-1/6)x(1-1/7)x(1-1/8)

This expression might seem daunting at first, but it simplifies quite nicely with a bit of observation. Let's break it down step-by-step:

Simplifying Each Term

  • (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
  • (1-1/7) = 6/7
  • (1-1/8) = 7/8

Now our expression looks like this:

(1/2) x (2/3) x (3/4) x (4/5) x (5/6) x (6/7) x (7/8)

Recognizing the Pattern

Notice that most of the terms cancel out! We have a lot of numerator and denominator pairs that simplify to 1.

  • 2 in the numerator of the first term cancels with 2 in the denominator of the second term.
  • 3 in the numerator of the second term cancels with 3 in the denominator of the third term.
  • And so on...

The Final Calculation

After all the cancellations, we are left with:

(1/8)

Therefore, the simplified value of the expression (1-1/2)x(1-1/3)x(1-1/4)x(1-1/5)x(1-1/6)x(1-1/7)x(1-1/8) is 1/8.

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