The Art of Mathematics

Help 6.4

or Sum — sum of series

1. Interface

Full version of the command looks like:

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


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

where index is summation index, start — index start value, finish — index finish value (inclusive), step — index step, expression — expression to evaluate for every index value and sum up. 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, 1/k);

is equivalent to



Sum(k, 2, 8, 2, 1/k);

is equivalent to


Double summation can be written down as nested sums:

(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

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