i know the limit should be 0 because the the series in the numerator is larger the the one in the denominator for every n

but i don't know how to start on proving it

help?

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- September 25th 2011, 11:15 AMidom87where do you suggest i start with this one (series limit)

i know the limit should be 0 because the the series in the numerator is larger the the one in the denominator for every n

but i don't know how to start on proving it

help? - September 25th 2011, 11:45 AMNOX AndrewRe: where do you suggest i start with this one (series limit)
I believe you mean the denominator is larger than the numerator; therefore, the limit is 0. Wouldn't proving (and then pointing out that the product of two larger numbers is larger than the product of two smaller numbers) suffice?

- September 25th 2011, 12:45 PMchisigmaRe: where do you suggest i start with this one (series limit)
You can start writing the limit as...

(1)

Now the limit (1) is called*infinite product*and a basic criterion exstablishes that if the infinite product is written in the form...

(2)

... where all the , then if the series...

(3)

... converges, then the infinite product (2) converges and if the (3) diverges, then the infinite product (2) tends to infinity if in (2) the sign is '+' and the infinite product tends to 0 if the sign in (2) is '-'. In Your case the series...

(4)

... diverges and the sign is '-', so that...

Kind regards

- September 25th 2011, 12:59 PMidom87Re: where do you suggest i start with this one (series limit)
can you do it without using products? i haven't gotten there yet

- September 25th 2011, 01:02 PMidom87Re: where do you suggest i start with this one (series limit)
your'e right i mixed that up that's what i meant

- September 25th 2011, 01:20 PMchisigmaRe: where do you suggest i start with this one (series limit)