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

```

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