lean_workbook_plus_4647

⚠️ 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.

Therefore, we are just looking for the least integer $n$ such that $\dfrac 1{n(n+1)} < \dfrac 1{2010}$ , which easily gives $n=\boxed{45} \implies \textbf{(A)}$ .

Why this node was retired

The posted statement is

theorem lean_workbook_plus_4647 :
  IsLeast {n : ℕ | (1 : ℝ) / (n * (n + 1)) < 1 / 2010} 45   :=  by sorry

Natural n=0 is admitted and real division by zero gives an artificially smallest solution.

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

Proposed corrected statement

Prove 45 is the least positive integer n satisfying 1/(n(n+1))<1/2010, with all fractions real.

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.