lean_workbook_plus_77527

⚠️ 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.

Find the exact value of the series $\sum\limits_{n=1}^{\infty}(-1)^{n}(\sqrt[n]{n}-1)$.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_77527 : ∑' n : ℕ, (-1 : ℝ)^n * (n^(1/n) - 1) = - 2   :=  by sorry

A fractional-looking exponent elaborates as natural-number division (usually zero), so the formal power is not the source root.

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

Proposed corrected statement

Study the naturally ordered real series ∑_{n≥1}(−1)ⁿ(exp(log n/n)−1). Restore the positive start index and real nth root, and determine its sum without asserting the unsupported value −2. Use convergence of ordered partial sums if it is only conditionally convergent.

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.