Is there a way to have Maple compute the limit of a recursive sequence? For example, the sequence below

a_n = (a_(n-1) +2)/(a_(n-1) + 3), a_1 =2

is bounded and montonically decreasing, thus has a limit, but Maple is not able to compute the limit. Any ideas?

I just encountered a very strange behavior when using DEplot. I want to generate a slopefield and solution curves. However, when I enter the command, only the arrows in the slopefield are showing. If I click on the plot where the solution curve should be, I see the outline of the curve. It's as if the curve isn't begin colored. I hope someone is able to replicate this behavior and suggest a fix. Thanks! (See attached file) 

I would like to create a single animated plot with two components.

The first component being an animation of the graph of r = 2*sin(theta) as theta varies from 0 to 2*Pi in the r-theta plane.

The second component is another animation, simultaneously showing how the graph of r=2*sin(theta) is generated in the polar coordinate system.

I am able to produce each component separately rather easily using the plots:-animate( ) command. What I am looking for is somehow being able to use ...

I would like to have Maple reproduce the well known result that the geometric power series with first term 1 and common ratio x, with |x|<1, converges to 1/(1-x). When I do:

sum(x^k,k=0..infinity);

I get - 1/(x-1). Which is okay, but is there a way to force Maple to produce 1/(1-x)?

Thanks!

I would like to define the "12 by 12" matrix A where a_{ij} = (i-1)^(j-1) using for loops. How can this be done? If for loops are not the most efficient way, any other suggestions are welcome! Thanks!