Re: Re: Summation problem

• To: mathgroup at smc.vnet.net
• Subject: [mg56689] Re: [mg56675] Re: [mg56621] Summation problem
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Wed, 4 May 2005 00:32:54 -0400 (EDT)
• References: <200505030926.FAA25663@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```The documentation for Sum says:

> New in Version 1; modified in 3.

Shouldn't it be  "in 3 and 5" ?

Andrzej Kozlowski

On 3 May 2005, at 18:26, Devendra Kapadia wrote:

>
> On Sat, 30 Apr 2005, jaropis wrote:
>
>> Why can't Mathematica sum:
>> Sum[I^n/n,{n,1,Infinity}]
>> and gives the (incorrect) answer, that this is divergent while it can
>> do:
>> Sum[I^(n+1)/n,{n,1,Infinity}]
>> correctly?
>>
>> Jaroslaw Piskorski
>>
> Hello Jaroslaw Piskorski,
>
> Thank you for reporting this problem with an infinite sum.
>
> This is caused by a failure to detect the conditional convergence
> of the sum in your first example, in Mathematica 5.
>
> A workaround for the problem is to replace 'I' by the symbolic
> quantity 'x' and then substitute 'x' with 'I', as shown below.
>
> ==========================================================
> In[1]:= \$Version
>
> Out[1]= 5.1 for Linux (February 20, 2005)
>
> In[2]:= Sum[x^n/n,{n,1,Infinity}]/.{x-> I}
>
> Out[2]= -Log[1 - I]
>
> In[3]:= N[%]
>
> Out[3]= -0.346574 + 0.785398 I
>
> In[4]:= NSum[I^n/n,{n,1,Infinity}]
>
> Out[4]= -0.346574 + 0.785398 I
>
> ============================================================
>
> Sorry for the inconvenience caused by this problem.
>