{"id":"W2107485085","doi":"10.1080/00207390500186149","title":"Sum of the <i>m</i> -th powers of <i>n</i> successive terms of an arithmetic sequence: <i> b <sup>m</sup> </i>  + ( <i>a</i>  +  <i>b</i> ) <i> <sup>m</sup> </i>  + (2 <i>a</i>  +  <i>b</i> ) <i> <sup>m</sup> </i>  + … + (( <i>n</i>  − 1) <i>a</i>  +  <i>b</i> ) <i> <sup>m</sup> </i>","year":2006,"lang":"he","type":"article","venue":"International Journal of Mathematical Education in Science and Technology","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"Royal Military College of Canada; Royal Ottawa Mental Health Centre","funders":"","keywords":"Mathematics; Sequence (biology); Arithmetic; Sums of powers; Combinatorics; Order (exchange); Operator (biology); Function (biology); Algebra over a field; Differential operator; Discrete mathematics; Pure mathematics","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0003428397,0.0005503884,0.0002870163,0.0009474921,0.0004018063,0.001087253,0.0005642594,0.0001946048,0.01180315],"category_scores_gemma":[0.001428604,0.0001492805,0.0003313737,0.0005744902,0.0007957928,0.0009538397,0.0005777222,0.0005007581,0.003678413],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0004100093,"about_ca_system_score_gemma":0.0007092299,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000388327,"about_ca_topic_score_gemma":0.001256025,"domain_scores_codex":[0.9996662,0.00004261854,0.00002839722,0.00004994459,0.0001755719,0.00003731363],"domain_scores_gemma":[0.9997451,0.00006976535,0.00005144832,0.00003455685,0.0000762366,0.00002286845],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.0003339633,0.0001228869,0.005553473,0.001293879,0.0001575378,0.002072473,0.001498023,0.01545549,0.1775422,0.482398,0.01855872,0.2950134],"study_design_scores_gemma":[0.00006746274,0.0006615666,0.02221447,0.0004904703,0.0002842536,0.006872585,0.0009595309,0.1312816,0.2668793,0.3697842,0.2003073,0.0001971149],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.289066,0.003288096,0.4491051,0.000685133,0.00139824,0.0001614177,0.0008495855,0.00111452,0.254332],"genre_scores_gemma":[0.7514634,0.002096741,0.1458859,0.0003174289,0.0007367031,0.0001712886,0.0009309207,0.0009330725,0.0974646],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01180315,"threshold_uncertainty_score":0.03948545,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01215304185761942,"score_gpt":0.3045828204917398,"score_spread":0.2924297786341204,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}