[R] Convergent series

[(Ted Harding)]

I don't think so -- as I understand it, what David is looking for is
a method for taking a specification for the general term in a series
(of indefinite length) and accumulating the sum of terms until a
convergence criterion is satisfied -- see his Mathematica-inspired
hypothetical example (in his later mail):

  x <- 2.232; sum(f = function(n) {x^n/factorial(n)}, lower = 0,
    upper = Inf, numeric.method = "HypergeometricTermZeilberger",
    verify.convergence = TRUE)

Your "Reduce" example simply takes a fixed input vector of given
finite length, and in fact is equivalent to

  sum(1/2^(1:10))
  # [1] 0.9990234

The result he would want is 1.0000000 (to within some "tol=..."),
from input "1/2^n" as an expression.

I've not seen anything generic for this kind of thing in R; though
one could fairly easily write a naive function to do it, modulo some
head-scratching about how to test for convergence (an appropriate
test would depend on what kind of series was being summed).

Ted.

On 15-Jul-10 08:21:59, Allan Engelhardt wrote:
> Not 100% if this is what you are looking for, but maybe Reduce("+", x) 
> will do it?  E.g.
> 
> Reduce("+", 1/2^(1:10))
># [1] 0.9990234
> 
> Hope this helps.
> 
> Allan
> 
> On 14/07/10 11:57, David Bickel wrote:
>> What are some reliable R functions that can compute the value of a 
>> convergent series?
>>
>> David
>>
> 
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Date: 15-Jul-10                                       Time: 10:28:00
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