lean_workbook_plus_59549

⚠️ Retired — specification defect

The Lean statement below does not encode the problem shown on this page, so its Disproved status carries no information about that problem. Do not import this node or use it as a dependency.

Prove that the closed form for $a_n$ in the recurrence relation $a_{n+1}=\frac{2a_n}{3a_n+4}$ is $a_n=\frac{2}{3(2^{n-1}-1)+2^{n-1}}$.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_59549 (a : ℕ → ℝ) (a0 : a 0 = 1) (a_succ : ∀ n, a (n + 1) = 2 * a n / (3 * a n + 4)) : ∀ n, a n = 2 / (3 * (2 ^ (n - 1) - 1) + 2 ^ (n - 1))   :=  by sorry

The source closed form and indexing do not match the prescribed initial value.

The recorded counterexample refutes the statement as encoded. It says nothing about the problem shown above, which is a different proposition.

Proposed corrected statement

With a₀=1 and aₙ₊₁=2aₙ/(3aₙ+4), prove aₙ=2/(5·2ⁿ−3).

Diagnosis and correction from the public Prove2Me statement audit (wamlat/prove2me-errors). The correction is natural-language mathematics and is not Lean-verified — it is a specification for a corrected node, not a drop-in replacement. No corrected replacement node exists yet.