[R] Infinite Series

[Don McKenzie]

but you get a different hide with sum vs. cumsum.  David is right if you want the sum of n terms.

> sum(1/(1:100)^2) - pi^2/6
[1] -0.009950167
> sum(1/(1:1000)^2) - pi^2/6
[1] -0.0009995002

etc.

> On Jul 24, 2015, at 7:24 PM, Janh Anni <annijanh at gmail.com> wrote:
> 
> Wow! So many (simpler) ways to skin a cat.  Thanks!
> 
> On Fri, Jul 24, 2015 at 8:07 PM, David Winsemius <dwinsemius at comcast.net>
> wrote:
> 
>> 
>> On Jul 24, 2015, at 4:37 PM, Janh Anni wrote:
>> 
>>> Hello Jeff,
>>> 
>>> Thanks a lot.  I tried it and see that it prints out the entire 100
>> partial
>>> sums, so I can take the last value as the partial sum for the first 100
>>> terms. Would there be any way cumsum can print only the nth partial sum,
>>> i.e. the last value in the array, instead of printing the entire array?
>>> Thanks again.
>> 
>> Wouldn't that just mean using sum instead of cumsum?????
>> 
>> Can even check the error from the analytical limit.
>> 
>>> sum(1/(1:100)^2) - pi^2/6
>> [1] -0.009950167
>> 
>> 
>>> 
>>> Joseph
>>> 
>>> On Fri, Jul 24, 2015 at 2:02 PM, Jeff Newmiller <
>> jdnewmil at dcn.davis.ca.us>
>>> wrote:
>>> 
>>>> Please reply-all so the mailing list stays in the loop.
>>>> 
>>>> cumsum(1/(1:100)^2)
>>>> 
>>>> gives you the partial sums up through i=100.
>>>> 
>> ---------------------------------------------------------------------------
>>>> Jeff Newmiller                        The     .....       .....  Go
>> Live...
>>>> DCN:<jdnewmil at dcn.davis.ca.us>        Basics: ##.#.       ##.#.  Live
>>>> Go...
>>>>                                     Live:   OO#.. Dead: OO#..  Playing
>>>> Research Engineer (Solar/Batteries            O.O#.       #.O#.  with
>>>> /Software/Embedded Controllers)               .OO#.       .OO#.
>> rocks...1k
>>>> 
>> ---------------------------------------------------------------------------
>>>> Sent from my phone. Please excuse my brevity.
>>>> 
>>>> On July 24, 2015 10:30:09 AM PDT, Janh Anni <annijanh at gmail.com> wrote:
>>>>> Hello Jeff,
>>>>> 
>>>>> Thank you so much for the suggestion,  I searched cumsum as suggested
>>>>> but
>>>>> not sure it is what I had in mind.  For instance if I had the infinite
>>>>> series:    [image: Inline image 1]
>>>>> 
>>>>> and want to compute the sum of the, say, first 100 terms, how could I
>>>>> use
>>>>> cusum to do that?
>>>>> 
>>>>> Thanks again,
>>>>> 
>>>>> Janh
>>>>> 
>>>>> 
>>>>> On Thu, Jul 23, 2015 at 11:51 PM, Jeff Newmiller
>>>>> <jdnewmil at dcn.davis.ca.us>
>>>>> wrote:
>>>>> 
>>>>>> ?cumsum
>>>>>> 
>>>> 
>>>>> 
>> ---------------------------------------------------------------------------
>>>>>> Jeff Newmiller                        The     .....       .....  Go
>>>>> Live...
>>>>>> DCN:<jdnewmil at dcn.davis.ca.us>        Basics: ##.#.       ##.#.  Live
>>>>>> Go...
>>>>>>                                     Live:   OO#.. Dead: OO#..
>>>>> Playing
>>>>>> Research Engineer (Solar/Batteries            O.O#.       #.O#.  with
>>>>>> /Software/Embedded Controllers)               .OO#.       .OO#.
>>>>> rocks...1k
>>>>>> 
>>>> 
>>>>> 
>> ---------------------------------------------------------------------------
>>>>>> Sent from my phone. Please excuse my brevity.
>>>>>> 
>>>>>> On July 23, 2015 8:23:39 PM PDT, Janh Anni <annijanh at gmail.com>
>>>>> wrote:
>>>>>>> Dear All,
>>>>>>> 
>>>>>>> Does anyone know of any R functions that compute partial sums of
>>>>>>> series?
>>>>>>> 
>>>>>>> Thanks in advance!
>>>>>>> 
>>>>>>> Janh
>>>>>>> 
>>>>>>>     [[alternative HTML version deleted]]
>>>>>>> 
>>>>>>> ______________________________________________
>>>>>>> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
>>>>>>> https://stat.ethz.ch/mailman/listinfo/r-help
>>>>>>> PLEASE do read the posting guide
>>>>>>> http://www.R-project.org/posting-guide.html
>>>>>>> and provide commented, minimal, self-contained, reproducible code.
>>>>>> 
>>>>>> 
>>>> 
>>>> 
>>> 
>>>      [[alternative HTML version deleted]]
>>> 
>>> ______________________________________________
>>> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
>>> https://stat.ethz.ch/mailman/listinfo/r-help
>>> PLEASE do read the posting guide
>> http://www.R-project.org/posting-guide.html
>>> and provide commented, minimal, self-contained, reproducible code.
>> 
>> David Winsemius
>> Alameda, CA, USA
>> 
>> 
> 
> 	[[alternative HTML version deleted]]
> 
> ______________________________________________
> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.