Solve equation with summation?

*To*: mathgroup at smc.vnet.net*Subject*: [mg122945] Solve equation with summation?*From*: Ivan <iveney at gmail.com>*Date*: Fri, 18 Nov 2011 06:21:48 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

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?