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Re: Incorrect Summation
*To*: mathgroup at smc.vnet.net
*Subject*: [mg129181] Re: Incorrect Summation
*From*: Bob Hanlon <hanlonr357 at gmail.com>
*Date*: Thu, 20 Dec 2012 03:20:05 -0500 (EST)
*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com
*Delivered-to*: l-mathgroup@wolfram.com
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*References*: <20121218073534.C7529694B@smc.vnet.net>
All four of the WA queries below (in Mathematica or at the WA website
(without quotes on web)) give me the same output with pods: Input
interpretation, Approximated sum (~~ 10.5895), and Partial sums (list
line plot with markers for upper bound 2 to 7). Although the web site
states that the Standard computation time was exceeded.
WolframAlpha["sum cos(log(log(k)))/log(k) for k from 2 to infinity"]
WolframAlpha["Sum[cos(log(log(k)))/log(k), {k, 2, infinity}]"]
WolframAlpha["Sum[Cos[Log[Log[k]]]/Log[k], {k, 2, Infinity}]"]
WolframAlpha["Sum[Cos[Log[E,Log[E,k]]]/Log[E,k], {k, 2, Infinity}]"]
NSum[Cos[Log[Log[k]]]/Log[k], {k, 2, Infinity}]
NIntegrate::ncvb: NIntegrate failed to converge to prescribed accuracy
after 9 recursive bisections in k near {k} = {4.81037*10^7}.
NIntegrate obtained -174036. and 139616.98122151854` for the integral
and error estimates. >>
-174030.
Table[{m, Sum[Cos[Log[Log[k]]]/Log[k], {k, 2, m}] // N}, {m,
Table[10^e, {e, 1, 6}]}]
{{10, 5.32934}, {100,
11.2959}, {1000, -22.5644}, {10000, -586.372}, {100000, -6597.24}, \
{1000000, -64461.3}}
Bob Hanlon
On Wed, Dec 19, 2012 at 5:01 AM, Murray Eisenberg <murray at math.umass.edu> wrote:
> What did you type, exactly, for Wolfram|Alpha? I tried several "obvious" things, e.g.,
>
> sum cos(log(log(k)))/log(k) for k from 2 to infinity
>
> but WA was unable even to interpret it correct as asking for the sum of an infinite series.
>
> On Dec 18, 2012, at 2:35 AM, amzoti <amzoti at gmail.com> wrote:
>
>> Hi All,
>>
>> can someone try this and see if it returns an incorrect result?
>>
>> Sum[Cos[Log[Log[k]]]/Log[k],{k,2,Infinity}]
>>
>> I tried it on WA and believe the result is incorrect.
>>
>> Thanks.
>
> ---
> Murray Eisenberg murray at math.umass.edu
> Mathematics & Statistics Dept.
> Lederle Graduate Research Tower phone 413 549-1020 (H)
> University of Massachusetts 413 545-2838 (W)
> 710 North Pleasant Street fax 413 545-1801
> Amherst, MA 01003-9305
>
>
>
>
>
>
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