According to the attached file "test" I would like to determine the limit of the function f(n,x) for n-->00 as an exercise. I'm asking for advice on using "rsolve". I also want to calculate the limit of sqrt((n/3))*f(n,x) for n-->00 using f(n,x) from the file "test". I also need help with this. (This isn't a school assignment ;-).)

test.mw

Using the attached problem, I want to calculate a term with a constraint that m is not equal to n. How do I insert general constraints into Maple?

test.mw

I'm doing something wrong again in the attached file. Please advise.

test.mw

For practice, I would like to calculate the left-hand limit according to the attached file. The computer does not finish. The result pi^2/6 is known from a calculation "on foot".

Download test.mwtest.mw

For the following task I only get the numerical solution 2.356... :
sum(n=1 to oo)[arctan(2/n^2)]
The known "closed" result is 3*pi/4.