The Art of Mathematics

Help 6.3

or Prod — product of series

1. Interface

Full version of the command looks like:

(index, start, finish, step, expression);


Prod(index, start, finish, step, expression);

where index is product index, start — index start value, finish — index finish value (inclusive), step — index step, expression — expression to evaluate for every index value and multiply by. If the index step is 1, which is usually the case, it could be omitted:

(index, start, finish, expression);

2. How to use

For instance:

(k, 2, 8, sin(k));

is equivalent to



Prod(k, 2, 8, 2, sin(k));

is equivalent to


Double product can be written down as nested ones:

(k, 1, 2, (n, 3, 4, k+n));

which is equivalent of


If step parameter is used, its sign makes no difference — step sign always evaluated from comparison of start and finish, if start is greater, the step sign is positive, if finish is greater than start then step sign is negative.

3. Support

Product of series is supported in professional version of the Librow calculator.