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.]]>

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

]]>]]>

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.]]>

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

]]>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

]]>Is there somethingissing from the explanation?

]]>(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

]]>lim n!/n^n

n->infinity]]>