>>> If it's a limit, just compute it for numbers as close as possible to 
>>> the limiting value (or really really big numbers if the limiting 
>>> value is infinite).  The closer (or the bigger) the number you 
>>> compute it for the closer your answer will be.
>>
>> Wouldn't that be increadibly unstable, numerically?
> 
> How much of a problem this is depends on the limit.

True enough.

>>>> But you can't compute an infinite product.
>>>
>>> If the product converges then you can by definition get an 
>>> arbitrarily good approximation by computing the product of the first 
>>> n terms for a large enough n.
>>
>> I don't see how that is the case.
>>
>> If you have an infinite *sum*, then as long as the terms get 
>> progressively more tiny and never get larger again, you can disregard 
>> all the terms after a certain point. But if you're taking a *product* 
>> then any term, anywhere in the series could radically alter the final 
>> result.
> 
> The same is true for a sum actually.  The point is proving that an 
> infinite sum or product *converges* is to show that this doesn't happen. 
>  Basically you show that the partial sums/products form a convergent 
> sequence (see the "Limit of a sequence" Wikipedia article I linked). 
> Then you know by definition that you can get a good approximation by 
> computing a large enough partial sum/product.
> 
> In the case of a sum this requires that the terms progressively get 
> closer to zero, for a product it'll require they get closer to one.

I guess it's just the case that an infinite sum or product can be 
convergent, and yet converge really, *really* slowly...

>>> Out of curiosity have you ever had a calculus class?
>>
>> I've never had *any* maths class!
>>
>> (Unless you count what we did at school. This simply involved filling 
>> out hundreds of thousands of pages of long-division problems over a 
>> 7-year period...)
>>
>> Hypothetically I shouldn't be able to do algebra at all...
> 
> That's too bad, it seems like you would have greatly enjoyed being able 
> to do some math that was more advanced than long division.

Well, I *did* go to a school for stupid people, after all...

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