The Art of Mathematics

# ∑ or Sum — sum of series

## 1. Interface

Full version of the command looks like:

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

or:

``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

``1/2+1/3+1/4+1/5+1/6+1/7+1/8``

and

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

is equivalent to

``1/2+1/4+1/6+1/8``

Double summation can be written down as nested sums:

``∑(k, 1, 2, ∑(n, 3, 4, k*n));``

which is equivalent of

``1*3+1*4+2*3+2*4``

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.