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Student[NumericalAnalysis]

 RateOfConvergence
 compute the rate of convergence of a sequence or function

 Calling Sequence RateOfConvergence(S, n, opts)

Parameters

 S - algebraic; the function or sequence n - name; the name of the indexing variable opts - (optional) equation(s) of the form keyword = value where keyword is isfunction; whether S is is a function or sequence

Options

 • isfunction = true or false
 Whether to find the rate of convergence of a sequence or a function.  If S is a function, isfunction must be set to true. By default, isfunction=false.

Description

 • The RateOfConvergence command computes the rate of convergence of a sequence or function.
 • If S is a function, the option isfunction must be set to true.
 • By default, the isfunction option is set to false.

Examples

 > $\mathrm{with}\left(\mathrm{Student}[\mathrm{NumericalAnalysis}]\right):$
 > $\mathrm{RateOfConvergence}\left(1+\frac{1}{n},n\right)$
 ${1}{+}{\mathrm{O}}{}\left(\frac{{1}}{{n}}\right)$ (1)
 > $\mathrm{RateOfConvergence}\left(\frac{1}{2}-\frac{1}{{n}^{2}},n\right)$
 $\frac{{1}}{{2}}{+}{\mathrm{O}}{}\left(\frac{{1}}{{{n}}^{{2}}}\right)$ (2)
 > $\mathrm{RateOfConvergence}\left({ⅇ}^{x},x,\mathrm{isfunction}=\mathrm{true}\right)$
 ${1}{+}{\mathrm{O}}{}\left({x}\right)$ (3)