lean_workbook_plus_4682

⚠️ 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.

Derive the formula for $v_n$ using the relationship $v_{n+1}-{v_n\over 2}={3\over 2}\left({1\over 2}\right)^n$.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_4682 (v : ℕ → ℝ) (h : ∀ n, v (n + 1) - v n / 2 = (3 / 2) * (1 / 2) ^ n) : ∀ n, v n = 3 - 3 * (1 / 2) ^ n   :=  by sorry

The proposed geometric-difference formula is not the solution of this recurrence.

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

Proposed corrected statement

Use v(n)=(v(0)+3n)/2^n, retaining the freely specified initial value.

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.