I have been looking at integrals of various summations of cos(m*pi) for m = 1, 2, 3, .....a specific n with limits -1 and 1.  Currently, when maple provides an answer it contains numerous terms of the form sin (m*pi) for some m.  Clearly all these terms should = 0 which would simplify the answer greatly, but maple does not seem to recognise this.  Is there a way of forcing maple to recognise that all these terms should be 0.  I have tried the eval, evalf and value functions but none of these seemed to help.

If i have a sequence of r[i+1] = 2r[i-1] + 3r[i] (where [i] represents subscript i) how do I use the 'do' function to go from the point where initially r[i-1] is, for example, 3 and r[i] is 4 to the point at which r[i-1] is first greater than 300 and find r[i+1] at this point. I hope this question makes sense! Thankyou

On Maple 11 Modern Version: If I have two parametric curves, say y = 4t + t^4 and x = 5t - 7t^2 how can I plot an equation such as (y'') * (x') + (3x'') with ' being differential and '' being second differential. I have tried it in numerous ways but get the following error message - "Warning, unable to evaluate the functions to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct". I have been trying to plot for t=-1..1. Thanks