Calculate a Sequence
Calculator for finite sequences. A sequence is a numbered list of values, produced by the calculation of a formula. As running variable, which is increased by 1 in each step, i is used. Only this variable may occur in the sequence term. The basic arithmetic operations + - * / are allowed, as well as the power function, like pow(2#i) for 2i. 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. The output of the sequence is displayed as table.
Examples:
- 2*i-1 returns every odd number.
- With m=1 and n=10, pow(i#2) (syntax for i²) gives the quadratic sequence 1, 4, 9, 16, 25, 36, 49, 64, 81, 100
A sequence itself is defined as a list of finite or infinite many values. These values can have arisen or been collected in any way. However, in order to calculate a sequence, a rule for the formation of these values is required, which specifies how they can be generated. A computable sequence has this in common with a mathematical function. However, generally continuous values are inserted into a function, and the results can be represented in a function graph. A sequence, on the other hand, consists of discrete, consecutively numbered objects. In the predefined sequence of square numbers, object number 1 is 1, number 2 is 4, number 3 is 9, and so on. A sequence always begins with the number 1 and continues with the natural numbers up to a certain value or to infinity, although infinity is obviously not an option here. There is nothing between two numbers in a sequence; there is no object in the sequence with, for example, the number 1.5, even though the quadratic function can easily calculate with 1.5.