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. > > Devendra Kapadia. > Wolfram Research, Inc. >

**References**:**Re: Summation problem***From:*Devendra Kapadia <dkapadia@wolfram.com>