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Question 26922: Comparison Direction, Nonnegativity and Reference Status Cannot Be Omitted

On this page
  1. Original question and givens
  2. Definition and scope
  3. Step-by-step derivation
  4. Reverse checks
  5. Result
  6. This question review and source binding

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R0052-26922 · q-20261015-advance-20261117-r01-series-comparison-test-0097

Original question and givens

Boundary mode=divergent_upper, positive scale=22. Give (mode, series_a_description, series_b_description, term_comparison, actual_series_status, divergence_inference_claim).

  • G001 — Boundary mode=divergent_upper, positive scale=22. Give (mode, series_a_description, series_b_description, term_comparison, actual_series_status, divergence_inference_claim).

Definition and scope

Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.

Step-by-step derivation

S001 · implies

Before

source roles = [series-comparison-boundary]

After

derived = [[mode, term_a, term_b, comparison, reference_status, inference]]

Conditions: none

List this operation/mode exact source field order without JavaScript.Keep Boolean,string and null roles distinct;do not pad fields or infer the interface from answer shape.

Step identifiers and dependencies

Rule: source_ordered_fields_without_JS · Uses: G001

S002 · implies

Before

source roles = [divergent_upper, 22]

After

derived = [divergent_upper, a_n=22/n^2, b_n=22/n, a_n<=b_n, b_diverges_but_a_converges, No]

Conditions: none

finite_sample is a scope statement,not a complete infinite witness.A divergent upper series cannot force a smaller one to diverge,e.g.1/n²<=1/n.Signed terms fail nonnegativity and unknown_reference lacks the reference status.No rejects this inference,not every underlying convergence claim.

Step identifiers and dependencies

Rule: Series_original_comparison_boundary_scope_and_direction · Uses: G001, S001

Reverse checks

  • S002 · premise_and_result_audit — Reverse-check the complete original data,types,field order and premises;finite audits are not formal proofs of infinite theorems.
  • S001 · premise_and_result_audit — Reverse-check the complete original data,types,field order and premises;finite audits are not formal proofs of infinite theorems.

Result

(divergent_upper, a_n=22/n^2, b_n=22/n, a_n<=b_n, b_diverges_but_a_converges, No)

The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.

This question review and source binding

Review date: 2026-10-26

Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.

Source hashes and review receipts
  • input commit: 0f7be61e2c22317a4075561dc822c87d881a50db
  • original question SHA-256: 7207a1eff4bd24878163d446e17927930bf2996293bb204b3a557b0437a78cc6
  • candidate record SHA-256: 1123ba9d1039c8a0126fcf85b1ab62babd0f69a53d41058e6f58bb56632becdf
  • semantic review receipt SHA-256: 729b25cbf6bf5cb1d07a21a511ae216ec5fdd54a4a7aa2f7c21156b81ff37252
  • question-first witness SHA-256: d1ab788770eaad04f986986e65afb0d55791e8a8c0d747e9a2b499f79fe78df2
  • Lean: NOT_RUN · human review: NOT_PERFORMED
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