Thanks, this is along the lines of what I was looking for!

Yes. However, I guess I should've been clearer on my question. I wanted to know, in general, if Maple can find limiting values of sequences defined recursively. What if I didn't know in advance the existence of a limit? Could Maple provide any insight?

Yes. However, I guess I should've been clearer on my question. I wanted to know, in general, if Maple can find limiting values of sequences defined recursively. What if I didn't know in advance the existence of a limit? Could Maple provide any insight?

@acer 

It is possible to change the color of the shaded region using the regionoptions=[color=your_color] option. 

I am aware of solutions similar to the ones you've mentioned, and I've found them to be very useful. I am wondering, though, why are those the only options? For such a fundamental problem, shouldn't Maple at least attempt to provide a solution to someone who might not be able to (or want to) write their own procedure? I am fine writing my own procedure to solve some specific problem. Not everyone is.

Thanks for your comments!

The problem is that 16.01 has been superceded by 16.02. As far as I can tell, 16.01 is no longer available via Maplesoft's update page.

The problem is that 16.01 has been superceded by 16.02. As far as I can tell, 16.01 is no longer available via Maplesoft's update page.

I was able to reinstall 16.00 (which fixes the issue), but now I'm at a loss as to how go about getting 16.01. Any ideas?

I was able to reinstall 16.00 (which fixes the issue), but now I'm at a loss as to how go about getting 16.01. Any ideas?

I'm (almost) too embarassed to say I wasn't using the same number of frames in both animations. I'm glad you mentioned frames.

I'm (almost) too embarassed to say I wasn't using the same number of frames in both animations. I'm glad you mentioned frames.

That is exactly what I wasn't doing. Thanks for your response.

That is exactly what I wasn't doing. Thanks for your response.

Thanks. I knew it had to be easy, but I was stuck in the mindset of what I had to programmatically.

Thanks. I knew it had to be easy, but I was stuck in the mindset of what I had to programmatically.

I can confirm the same behavior in Maple 16. Other computer algebra systems are able to compute the definite integral. Will be interesting to see why.

Maple 16 is able, however, to compute the numerical approximation of the integral using evalf().