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## Topic review (newest first)

SteveB
2013-08-17 17:09:45

I agree with Bob. My only criticism was a lack of clarity of the argument. I knew what you meant and it is okay as
a proof provided:
(1) The result concerning (1/n) is proven earlier in the course and can be used by referring to it (it should be usually).
(2) The fraction has to be trapped below a certain positive constant. In this case it is obviously one or less.
Each term is between zero and one, including a term equaling one.
Proving bobbym's identities looks difficult to me, so if the question is an exercise in proving things then they might be
challenges to go on to if the proof of the first problem was too easy.

bob bundy
2013-08-17 07:46:01

I have shown that the product can be written

As 1/n tends to zero as n tends to infinity, I claim the product tends to zero times something finite and therefore to zero.

What's wrong with that?

Bob

bobbym
2013-08-17 05:46:32

Hi;

SteveB
2013-08-17 05:27:29

Maybe you should use the fact that (1/n) is one of the terms of the product and all of the others are one or less.
Then use the fact that if you multiply by a number between zero and one it reduces a positive number or keeps
it the same when it is equal to one.
Then I think you can make Bob's deduction.
In a formal proof that needs to be written out correctly. If you are doing a pure maths related course, then I
should do the rest as an exercise, mukesh, if you just copy someone else's version then you won't understand it.
anonimystefy: I agree. Strictly speaking in a formal proof that probably isn't enough. Suppose the product sequence
converges to one with increasing density, as n inreases, all near to one. The product could converge to a higher number.

anonimnystefy
2013-08-17 05:00:04

Typing issues, sorry.

The last sentence of your explanation doesn't follow from the rest.

bob bundy
2013-08-17 02:15:06

hi Stefy

Is there somethingissing from the explanation?

aybe.  y posts often have things issing.  But what would you like e to include?

I'd put in an 'm' if I could think of a suitable place for it.

Bob

anonimnystefy
2013-08-17 01:58:41

Hi Bob

Is there somethingissing from the explanation?

bob bundy
2013-08-10 22:02:09

(capital pi symbol is for 'the product of' )

i/n ≤1 => the product is less than 1

as n approaches infinity 1/n approaches zero = the limit tends to zero

Bob

bobbym
2013-08-10 21:30:08

Intuitively obvious that it approaches 0.

ShivamS
2013-08-10 11:49:05

Consider the simplification: limit of x! * x^-x as x approaches infinity. After it's some expansion of the series which will make you cry without a math pack.

mukesh
2013-08-10 10:45:21

hw?i didnt undrstand

ShivamS
2013-08-10 10:34:09

0.

mukesh
2013-08-10 10:24:14

evaluate
lim n!/n^n
n->infinity