Summation Calculator

Sigma notation is handled by parsing the expression once and then evaluating it for every value of the index between the two bounds. You can use the index variable, decimal numbers, pi and e, brackets, the four arithmetic operators, powers, and the functions sqrt, abs, ln, log, exp, sin, cos, tan, floor and ceil, with angles in radians. Separate modes use the closed forms for an arithmetic or a geometric series, which stay exact for large term counts and also say whether an infinite geometric series converges. A fourth mode just adds up a list you paste in, and reports the count, mean, smallest and largest alongside the total. Terms are capped at twenty thousand, and an expression with no value somewhere in the range is reported rather than quietly skipped.