The value of
2023
The value of
- A.
n-1/n
- B.
1/n
- C.
1/n+1
- D.
More than one of the above
- E.
None of the above
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Correct answer: B
To find the value of the given expression, we first simplify each term inside the parentheses.
The expression is: (1 - 1/2)(1 - 1/3)(1 - 1/4)...(1 - 1/n)
Simplifying each term gives: (1/2)(2/3)(3/4)...((n-1)/n)
This is a telescoping product. The numerator of each fraction cancels with the denominator of the previous fraction. For example, the 2 in the numerator of the second term cancels with the 2 in the denominator of the first term.
After all cancellations, only the numerator of the first term (1) and the denominator of the last term (n) remain.
Thus, the value of the expression is 1/n.
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