It would be very nice if Maple could handle true infinite sequences. In addition to basic operations performed elementwise between two (or more) sequences, it should be possible to:
- plot a sequence
- determine if the sequence converges
Note that the seq command (and the list datatype) can be used only for FINITE sequences. Also, the current limit command assumes the independent variable is continuous - not discrete.
Here's a simple example of what I would like to be able to do:
> S := Seq( sin(n*Pi), n=1..infinity );
> plot( S, view=[1..100,DEFAULT] );
> L := Limit( S, n, type='Sequence' );
> L = value(L);
I am well aware of how this particular example can be completed in Maple 10. What I am requesting is a more convenient, robust, and integrated implementation that would be suitable for use with students in Calculus II.
Maybe the appropriate place for these revisions to appear is the Student package. Either there should be a separate Calculus2 package or the current Calculus1 subpackage should be renamed Student[Calculus]. (I will not accept the explanation that the "1" in Calculus1 refers to "single-variable" calculus. This is NOT the way students see it.)