On Monday, 4 Dec 2006, Daniel Lakeland wrote:
> On Sun, Dec 03, 2006 at 08:49:50PM +0000, Leo wrote:
>> Hi all,
>>
>> I am learning maxima. I want to use it to get the value of the
>
>> following when n goes to infinity.
>>
>> n
>> ====
>> \ 1
>> > -----------
>> / sqrt(n + i)
>> ====
>> i = 1
>> -----------------
>> sqrt(n)
>
> I'm sure you've tried just taking the limit using the "limit"
> function. This doesn't work.
>
> So you'll have to resort to some mathematics which maxima can help you
> with. Does the limit exist?
>
> You could compare it to the following integral:
>
> integrate(1/sqrt(n) * 1/(sqrt(n+i)),i,0,n);
>
> maxima will calculate this and take the limit as n -> inf
>
> Perhaps this will help you.
That did help with this question. I was expecting a more general
solution because there are just too many such questions. For example,
n
====
\ 1
> --
/ 2
==== i
i = 1
How can I get the limit when n -> inf?
Thanks.
--
Leo