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Package series (in series.i) -

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DOCUMENT series_n(r, s) returns the minimum number n of terms required for the geometric series 1 + r + r^2 + r^3 + ... + r^n = s to reach at least the given value s. An alternate viewpoint is that n is the minimum number of terms required to achieve the sum s, with a ratio no larger than r. Returns 0 if r<1 and s>1/(1-r), or if s<1. The routine makes the most sense for r>1 and s substantially greater than 1. The intended use is to determine the minimum number of zones required to span a given thickness t with a given minimum zone size z, and maximum taper ratio r (assumed >1 here): n= series_n(r, t/z); With this n, you have the option of adjusting r or z downwards (using series_r or series_s, respectively) to achieve the final desired zoning. R or S or both may be arrays, as long as they are conformable.

DOCUMENT series_r(s, n) returns the ratio r of the finite geometric series, given the sum s: 1 + r + r^2 + r^3 + ... + r^n = s Using n<0 will return the the reciprocal of n>0 result, that is, series_r(s, -n) == 1.0/series_r(s, n) If n==0, returns s-1 (the n==1 result). S or N or both may be arrays, as long as they are conformable.