Re: Why this can't be reduced by mathematica?!

*To*: mathgroup at smc.vnet.net*Subject*: [mg114150] Re: Why this can't be reduced by mathematica?!*From*: Valeri Astanoff <astanoff at gmail.com>*Date*: Thu, 25 Nov 2010 05:58:02 -0500 (EST)*References*: <iciul1$leo$1@smc.vnet.net>

On Nov 24, 12:58 pm, olfa <olfa.mra... at yahoo.fr> wrote: > Hi Mathematica Community, > > Reduce[s==Sum[a[index], {index, i + 1, N}] - Sum[a[index], {index, j = + > 1, N}] && > j >= i,{s}] > > the output should be s==Sum[a[index], {index, i+1, j }] > > but it is not! > Thank you. Good day, You can do it this way : In[1]:= myCombine[Sum[a_, {i_, i1_, i2_}] - Sum[a_, {i_, j1_, j2_}]] := Sum[a, {i, Min[i1, j1], Max[i1, j1] - 1}] + Sum[a, {i, Min[i2, j2] + 1, Max[i2, j2]}] In[2]:= s = Sum[a[index], {index, i + 1, n}] - Sum[a[index], {index, j + 1, n}]; In[3]:= s // myCombine // Simplify[#, j >= i] & Out[3]= Sum[a[index], {index, 1 + i, j}] -- Valeri