# Calculate the Sum

Calculator for the summation with the sum symbol Sigma, Σ. The sum is a repeated addition with a start value m and an end value n. As running variable, which is increased by 1 in each step, i is used, this must be an integer. Only this variable may occur in the sum term. The basic arithmetic operations + - * / are allowed, as well as the power function, like pow(2#i) for 2^{i}. Further allowed functions are sin(), cos(), tan(), asin(), acos(), atan(), log() for the natural logarithm and fac() for the factorial. Also, the constants e and pi can be used.

1/fac(i) with m=0 is one definition of Euler's number e.

An infinite sum is called series.

The sum sign is used when several numbers specified by a rule are to be added. In the example above with Σ i, the rule is simply to always take the next number. This sum continues to grow, and the faster it progresses. A sum that grows more slowly over time is, for example, Σ 1/i. Of course, a minus in front of the summand ensures that the sum becomes smaller. With a (-1)^{i}, written here as pow(-1#i), you can add and subtract the summands alternately.

Sums and products, series and sequences are used very frequently in mathematics; they are relatively easy to calculate and offer solutions to numerous problems. Their writing seems unusual and therefore complicated, but it is fairly easy to understand. The use of the large Greek letter Sigma for the sum goes back to Leonhard Euler in 1755; the lower limit and upper limit (here m and n) were added by Joseph Fourier in 1829.