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Bob say: It's one more than you had before, so if n = 3 apples, n+1 = 4 apples, OK?
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Amy say: Not quite.
(n+1)! = (n+1)(n)(n-1)!
(n+1)! = (n+1)(n)(n-1)(n-2)(n-3)....(3)(2)(1)
But (n-1)(n-2)(n-3)....(3)(2)(1) = (n-1)!
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Sakai Saburo say: Lhs#0--->rhs#0
--->n>=2
(i) n=2 is ok
(ii) n>2 divide both sides by (n-1)n(n+1)
--->(n-2)!=1
---> n=3
solutions : 2,3
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Captain Matticus, LandPiratesInc say: (n + 1)! = (n + 1) * n * (n - 1) is not an identity.
However, if you want it worked out:
(n + 1)! =>
(n + 1) * n * (n - 1) * (n - 2) * .... * 3 * 2 * 1
If (n + 1)! = (n + 1) * n * (n - 1), then:
(n + 1) * n * (n - 1) * (n - 2)! = (n + 1) * n * (n - 1)
(n - 2)! = 1
n - 2 = 0 , 1
n = 2 , 3
Test:
(3 + 1)! = 4! = 24
(3 + 1) * 3 * (3 - 1) = 4 * 3 * 2 = 24
(2 + 1)! = 3! = 6
(2 + 1) * 2 * (2 - 1) = 3 * 2 * 1 = 6
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D.W. say: n = 3
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Daniel say: n=3
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M. say: One more!
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Myles say: (n+1)! = (n+1)(n)(n-1).....(2)(1)
Like all factorials.
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