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Solve equation with summation?


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?



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