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Your rv does not consists solely of variables. Some elements are products of variables. Do you want the products treated as if they were single variables or rather split into the separate variables?
@yarchik - It was documented in V7 (perhaps earlier?). See reference.wolfram.com/legacy/v7/ref/Solve.html While no longer documented, it still works. You can emulate this by also using Eliminate
Or Solve[{b + c - a - d == 0, 2 b - a + c == 0, c - e == 0}, {b, d}, {c}] or Solve[{b + c - a - d == 0, 2 b - a + c == 0, c - e == 0}, {b, d}, MaxExtraConditions -> 1]
Reversing the order of the summation also works here:F1 = Simplify[Sum[16^j/(4 + 16^j), {j, a, b, c}] /. {a -> 1/2025, b -> 2024/2025, c -> 1/2025}]; F2 = Simplify[Sum[16^j/(4 + 16^j), {j, b, a, -c}] /. {a -> 1/2025, b -> 2024/2025, c -> 1/2025}]; (F1 + F2)/2 // FullSimplify