Graph Software for Scientists and Engineers

SUM(expression)

Adds the result of the argument to the previous result. This function is useful for evaluating Taylor series.

The SUM function differs from all other functions in 2 respects:

You are limited to 10 SUM functions in any equation (or pair of equations in the case of X=f(T),Y=g(T)).

The Prevent divide by zero errors feature of the Y=f(X) command and similar commands must be ignored when SUM is used in an equation. Division by 0 or other math error will result in an error message rather than incrementing X by a small value and re-evaluating.

Example

A well-known (though very slow to converge) method for calculating π is:

which can be expressed in DPlot as:

4*sum(((-1)^(x+1))/(2*x-1))

The mathematician and astronomer Madhava of Sangamagrama found a series that converges much faster than the above:

which may be expressed in DPlot as

sqrt(12)*sum(((-1)^(x+1))/((2*x-1)*3^(x-1)))

The first 20 terms of both series result in:

Taylor series approximations of PI

See also:

Trigonometric and General Math Functions

$
195.
00
 
RUNS ON
Windows 10,
Windows 8,
Windows 7, 2008,
Vista, XP, NT,
ME, 2003, 2000,
Windows 98, 95
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