Understanding the (1+1/n)^n Problem: The Last Term in Binomial Expansion

[MathematicalPhysicist]

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).

 

[benorin]

(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

 

[MathematicalPhysicist]

okay i think i can see it, thanks.