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6 Answers
- frankLv 78 years ago
by definition :
0! = 1 and,
x! = x(x-1)(x-2)(x-3)...3x2x1
x! = x(x-1)!
so, (x-1)!/x! = 1/x
(x-1)!/(x-1)! = 1/x
1 = 1/x
1/1 = 1/x (crossed product)
x = 1 (answer)
verification => (x -1)!/(x!) = (1/x)
(1-1)!/(1!) = 1/1
0!/(1!) = 1
1/1 = 1
1 = 1
- 8 years ago
(x - 1)! = (x - 1)(x - 2)(x - 3)...(2)(1)
(x)! = x(x - 1)(x - 2)(x - 3)...(2)(1)
So, (x - 1)! / (x)! cancels out all terms, besides x, which is on the denominator, hence 1 / x
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- ?Lv 78 years ago
(x - 1)! = (x - 1)(x - 2)(x - 3)....1
x! = x(x - 1)(x - 2)(x - 3)....1
so, (x - 1)! cancels to leave 1/x
:)>
- 8 years ago
because (x - 1)! / x (x - 1)! ..............[ as x! is same as x (x - 1) !]
=> after cancelling out (x-1)! you'll have 1 / x.
