lean_workbook_plus_45614

⚠️ Retired — specification defect

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

Evaluate the infinite series: $\frac24 + \frac{4}{16} + \frac{6}{64} + \frac{8}{256} + \cdots + \frac{2n}{4^n}$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_45614 (n : ℕ) : (∑' n : ℕ, (2 * n) / (4 ^ n)) = 2 / 3   :=  by sorry

The entire series is interpreted in ℕ and all terms vanish; the inserted real sum2/3 is also wrong.

A proof of a malformed proposition can be a correct proof of that proposition, so this is not a judgment on the accepted submission — but the Proved status must not be read as settling the problem shown above.

Proposed corrected statement

Over ℝ prove HasSum(n↦2n/4^n)(8/9), with n cast toℝ before division. The n=0 term is0, so the positive-index source has the same sum.

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.