Quiz — 6338ddd0ba611_Suite divergente.pdf

Question 1 sur 10 20:00

[{"id":85450,"question":"Quelle est la limite de la suite définie par uₙ = n² pour n → +∞ ?","option_a":"0","option_b":"+∞","option_c":"-∞","option_d":"1","option_e":"","option_f":"","bonne_reponse":"b","explication":"La suite uₙ = n² tend vers +∞ lorsque n tend vers +∞, donc 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\": \"0\", \"b\": \"+∞\", \"c\": \"-∞\", \"d\": \"1\"}}","_debug_options_count":4},{"id":85451,"question":"Une suite oscillante entre -1 et 1 est-elle convergente ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une suite oscillante sans limite n'est pas convergente, même si elle reste bornée.","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":85452,"question":"Quelle méthode permet de prouver la divergence d'une suite ?","option_a":"Utiliser le théorème des gendarmes","option_b":"Montrer que la limite est infinie","option_c":"Appliquer le théorème de Pythagore","option_d":"Calculer la moyenne des termes","option_e":"","option_f":"","bonne_reponse":"b","explication":"Montrer que la limite d'une suite est infinie est une méthode directe pour prouver sa divergence.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Utiliser le théorème des gendarmes\", \"b\": \"Montrer que la limit","_debug_options_count":4},{"id":85453,"question":"La suite uₙ = (-1)ⁿ est-elle convergente ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La suite uₙ = (-1)ⁿ oscille entre -1 et 1 sans se stabiliser, donc 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":85454,"question":"Si une suite uₙ vérifie uₙ ≤ vₙ pour tout n et que vₙ converge vers 0, que peut-on dire de uₙ ?","option_a":"uₙ converge vers 0","option_b":"uₙ est divergente","option_c":"uₙ est bornée","option_d":"On ne peut rien conclure","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le théorème des gendarmes permet de conclure que uₙ converge vers 0 si uₙ ≤ vₙ ≤ wₙ et que vₙ et wₙ convergent 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\": \"uₙ converge vers 0\", \"b\": \"uₙ est divergente\", \"c\": \"uₙ est","_debug_options_count":4},{"id":85455,"question":"Quelle est la limite de la suite uₙ = (1 + 1\/n)ⁿ pour n → +∞ ?","option_a":"0","option_b":"1","option_c":"e","option_d":"+∞","option_e":"","option_f":"","bonne_reponse":"c","explication":"La suite uₙ = (1 + 1\/n)ⁿ converge vers le nombre e ≈ 2,718, donc elle est convergente.","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\": \"e\", \"d\": \"+∞\"}}","_debug_options_count":4},{"id":85456,"question":"Une suite bornée est-elle toujours convergente ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une suite bornée n'est pas nécessairement convergente (exemple : la suite uₙ = (-1)ⁿ).","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":85457,"question":"Quelle propriété permet de comparer deux suites pour étudier leur divergence ?","option_a":"Le théorème de Thalès","option_b":"Le théorème de comparaison","option_c":"Le théorème de Pythagore","option_d":"Le théorème de Gauss","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le théorème de comparaison permet d'étudier la divergence en comparant les termes de deux suites.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Le théorème de Thalès\", \"b\": \"Le théorème de comparaison\", \"","_debug_options_count":4},{"id":85458,"question":"La suite uₙ = n\/(n+1) est-elle convergente ? Si oui, vers quelle limite ?","option_a":"Non, elle est divergente","option_b":"Oui, vers 0","option_c":"Oui, vers 1","option_d":"Oui, vers +∞","option_e":"","option_f":"","bonne_reponse":"c","explication":"La suite uₙ = n\/(n+1) converge vers 1 lorsque n tend vers +∞, donc elle est convergente.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"Non, elle est divergente\", \"b\": \"Oui, vers 0\", \"c\": \"Oui, vers 1\"","_debug_options_count":4},{"id":85459,"question":"Si une suite uₙ vérifie uₙ ≥ vₙ pour tout n et que vₙ diverge vers +∞, que peut-on dire de uₙ ?","option_a":"uₙ converge","option_b":"uₙ diverge vers +∞","option_c":"uₙ est bornée","option_d":"On ne peut rien conclure","option_e":"","option_f":"","bonne_reponse":"b","explication":"Si uₙ ≥ vₙ et que vₙ diverge vers +∞, alors uₙ diverge également vers +∞.","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 converge\", \"b\": \"uₙ diverge vers +∞\", \"c\": \"uₙ est bor","_debug_options_count":4}]