Quiz — سلسلة تمارين في المتتاليات1.docx

Question 1 sur 10 20:00

[{"id":7415,"question":"Quelle est la formule générale d'une suite arithmétique de raison r ?","option_a":"Uₙ = U₀ + n","option_b":"Uₙ = U₀ + n·r","option_c":"Uₙ = U₀·rⁿ","option_d":"Uₙ = U₀ + rⁿ","option_e":"","option_f":"","bonne_reponse":"b","explication":"La formule générale d'une suite arithmétique est Uₙ = U₀ + n·r, où U₀ est le premier terme et r la raison.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Uₙ = U₀ + n\", \"b\": \"Uₙ = U₀ + n·r\", \"c\": \"Uₙ = U₀·r","_debug_options_count":4},{"id":7416,"question":"Une suite géométrique de raison q = 1 est convergente.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une suite géométrique de raison q = 1 est constante (Uₙ = U₀) et donc convergente vers U₀.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":7417,"question":"Soit une suite définie par Uₙ₊₁ = 2Uₙ + 1 avec U₀ = 0. Quelle est la valeur de U₂ ?","option_a":"3","option_b":"5","option_c":"7","option_d":"9","option_e":"","option_f":"","bonne_reponse":"c","explication":"U₁ = 2·0 + 1 = 1, U₂ = 2·1 + 1 = 3. La valeur de U₂ est 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"3\", \"b\": \"5\", \"c\": \"7\", \"d\": \"9\"}}","_debug_options_count":4},{"id":7418,"question":"La suite (Uₙ) définie par Uₙ = (-1)ⁿ est convergente.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La suite (Uₙ) alterne entre -1 et 1, donc elle n'a pas de limite. Elle est divergente.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":7419,"question":"Quel est le terme général d'une suite géométrique de premier terme U₀ et de raison q ?","option_a":"Uₙ = U₀ + n·q","option_b":"Uₙ = U₀·qⁿ","option_c":"Uₙ = U₀ + qⁿ","option_d":"Uₙ = U₀·n","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le terme général d'une suite géométrique est Uₙ = U₀·qⁿ, où U₀ est le premier terme et q la raison.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Uₙ = U₀ + n·q\", \"b\": \"Uₙ = U₀·qⁿ\", \"c\": \"Uₙ = U₀ ","_debug_options_count":4},{"id":7420,"question":"La suite (Uₙ) définie par Uₙ = n² \/ (n + 1) a pour limite :","option_a":"0","option_b":"1","option_c":"∞","option_d":"n","option_e":"","option_f":"","bonne_reponse":"c","explication":"En divisant le numérateur et le dénominateur par n, on obtient Uₙ = n \/ (1 + 1\/n). La limite est donc ∞.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"0\", \"b\": \"1\", \"c\": \"∞\", \"d\": \"n\"}}","_debug_options_count":4},{"id":7421,"question":"Une suite croissante et majorée est toujours convergente.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une suite croissante et majorée est convergente (théorème de la limite monotone).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":7422,"question":"Soit une suite arithmétique de premier terme U₀ = 5 et de raison r = -2. Quel est le terme U₅ ?","option_a":"-5","option_b":"-3","option_c":"3","option_d":"5","option_e":"","option_f":"","bonne_reponse":"a","explication":"U₅ = U₀ + 5·r = 5 + 5·(-2) = 5 - 10 = -5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"-5\", \"b\": \"-3\", \"c\": \"3\", \"d\": \"5\"}}","_debug_options_count":4},{"id":7423,"question":"La suite (Uₙ) définie par Uₙ = (n² + 1)\/n a pour limite :","option_a":"0","option_b":"1","option_c":"∞","option_d":"n","option_e":"","option_f":"","bonne_reponse":"c","explication":"En simplifiant, Uₙ = n + 1\/n. La limite est donc ∞.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"0\", \"b\": \"1\", \"c\": \"∞\", \"d\": \"n\"}}","_debug_options_count":4},{"id":7424,"question":"Une suite géométrique de raison q telle que |q| \u003C 1 est convergente.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une suite géométrique de raison q avec |q| \u003C 1 converge vers 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4}]