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Re: Solve equation with summation?

• To: mathgroup at smc.vnet.net
• Subject: [mg123041] Re: Solve equation with summation?
• From: Dana DeLouis <dana.del at gmail.com>
• Date: Mon, 21 Nov 2011 04:28:43 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

Hi.  A simpler example than Solve for this issue might be to just multiply.

t = Sum[Subscript[a, i]/x, {i, 1, n}]

If you multiply the above by x, then the x should cancel.

However, it still remains unevaluated.  

FullSimplify[x*t]

x*Sum[Subscript[a, i]/x, {i, 1, n}]

As a side note, saying that x was not zero didn't help either.

x * Sum[Subscript[a, i]/x, {i, 1, n}, Assumptions -> x != 0]
<unevaluated>

Because if x was zero, then you have  Power::Infy

Sum[Subscript[a, i]/0, {i, 1, n}]

Power::infy:Infinite expression 1/0 encountered. >>
ComplexInfinity

= = = = = = =



On Nov 18, 6:22 am, Ivan <ive... at gmail.com> wrote:
> For a summation like \sum_{i=1}^n a_i/x = 1,
> 
>   Solve[Sum[Subscript[a, i], {i, 1, n}]/x == 1, x]
> 
> gives a correct solution.
> 
> However, by putting x into the summation:
> 
>   Solve[Sum[Subscript[a, i]/x, {i, 1, n}] == 1, x]
> 
> gives an empty set, why?

• Follow-Ups:
  • Re: Solve equation with summation?
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>