(1+1/n)^n problem

  • #1
MathematicalPhysicist
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it's rather a bypass question, not a direct question about 'e'.

the last term in the binomial expansion of (1+1/n)^n is according to my text:
(1/n!)(1-1/n)(1-2/n)....(1-(n-1)/n)
while it should be (1/n!)(n(n-1)...1)/n^n

okay, these two terms are almost identical, the first equals
(with disregarding of 1/n!):
((n-1)(n-2)...1)/n^n
and second one is the first multiplied by n, then what is the problem.

i assume it's with me ( just kidding).
 

Answers and Replies

  • #2
benorin
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(1/n!)(1-1/n)(1-2/n)....(1-(n-1)/n)
= (1/n!)(n-1)(n-2)....(n-(n-1))/n^(n-1)
= (1/n!)(n-1)...1/n^(n-1)
= (1/n!)(n(n-1)...1)/n^n

so, they're the same
 
  • #3
MathematicalPhysicist
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okay i think i can see it, thanks.
 

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