x(1-1%2F3)x(1-1%2F4)x(1-1%2F5)x(1-1%2F6)x(1-1%2F7)x(1-1%2F8).jpeg "(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.