∏() is used to multiply a sequence of numbers. ∏(expression, variable, start, end) will evaluate expression for variable=start, then for variable=start+1, all the way through variable=end, and multiply the results:
:∏(f(x),x,1,5) f(1)*f(2)*f(3)*f(4)*f(5) :∏(x,x,1,5) 120
In this way, ∏() is no different from taking product() of a sequence generated by seq(). However, ∏() can be used for more abstract calculations — for instance, when start or end is an undefined variable, it will try to find the product in terms of that variable. ∏() can also be used to find the product of an infinite series (just make the value of end infinity — ∞).
:∏(x,x,1,n) n! :∏(1-1/x,x,2,n) 1/n