Summation

Maple allows you to specify both definite and indefinite symbolic
summations using the sum command:

> # Be sure that the index variable is a mathematical variable.
> # If i had a value (say, 3), it would be meaningless to say
> # something like "sum 3 squared for 3 from 1 to n" when you meant to
> # say "sum i squared for i from 1 to n":
> i;
i
> # This is an example of a sum over an indefinite (non-negative)
> # index range:
> x; # Just to be sure, we want to see if x is a mathematical variable.
x
> sum(x^i, i);
   i
  x
-----
x - 1
> # These are examples of definite sums:
> sum(i, i = -2 .. 5);
12
> sum(x**i, i = 0 .. 3);
         2    3
1 + x + x  + x