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Re: Sum simplifying

  • To: mathgroup at smc.vnet.net
  • Subject: [mg89223] Re: [mg89200] Sum simplifying
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Fri, 30 May 2008 02:55:29 -0400 (EDT)
  • Reply-to: hanlonr at cox.net

sub = (Sum[a_. * x_ + y_., {k_, lower_, upper_}] /; FreeQ[a, k]) :>
    a*Sum[x, {k, lower, upper}] + Sum[y, {k, lower, upper}];

expr = Sum[a[k]*I + b[k], {k, 1, n}] -
   I*Sum[a[k], {k, 1, n}] - Sum[b[k], {k, 1, n}];

expr /. sub

0


Bob Hanlon

---- Lari <lari.jarvenpaa at luukku.com> wrote: 
> Hey,
> 
> I'd like to simplify a following type of sum:
> 
> In[62]:= Sum[a[k]*I + b[k], {k, 1, n}] - I*Sum[a[k], {k, 1, n}] - 
>  Sum[b[k], {k, 1, n}]
> 
> In[63]:= FullSimplify[%]
> 
> The result should obviously be zero; however, Mathematica returns the same expression. If I put n an integer value it knows how to simplify. How do I make it understand that also with a symbolic upper limit?
> 
> Hope someone can help!
> 
> Thanks,
> Lari
> 



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