how to solve this limit problem?



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