Quiz — 661e8fc99002b_énoncé_Série-N°41(suites ).pdf

Question 1 sur 10 20:00

[{"id":61117,"question":"Quelle est la raison d'une suite arithmétique dont les termes sont : 3, 7, 11, 15, ... ?","option_a":"2","option_b":"4","option_c":"3","option_d":"5","option_e":"","option_f":"","bonne_reponse":"b","explication":"La raison d'une suite arithmétique est la différence entre deux termes consécutifs. Ici, 7 - 3 = 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"2\", \"b\": \"4\", \"c\": \"3\", \"d\": \"5\"}}","_debug_options_count":4},{"id":61118,"question":"Une suite géométrique de raison q = 2 et de premier terme u₀ = 1 est-elle 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| \u003E 1 est divergente. Ici, q = 2 \u003E 1, donc la suite diverge.","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":61119,"question":"Quelle est la limite de la suite définie par uₙ = (3n + 1)\/n pour n tendant vers l'infini ?","option_a":"3","option_b":"0","option_c":"1\/3","option_d":"1","option_e":"","option_f":"","bonne_reponse":"a","explication":"En divisant numérateur et dénominateur par n, on obtient uₙ = 3 + 1\/n. Lorsque n tend vers l'infini, 1\/n tend vers 0, donc la limite est 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"3\", \"b\": \"0\", \"c\": \"1\/3\", \"d\": \"1\"}}","_debug_options_count":4},{"id":61120,"question":"Le théorème des gendarmes s'applique-t-il à la suite définie par uₙ = sin(n)\/n ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Oui, car -1\/n ≤ sin(n)\/n ≤ 1\/n, et les suites -1\/n et 1\/n convergent toutes deux vers 0. Par le théorème des gendarmes, uₙ converge aussi 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},{"id":61121,"question":"Quelle est la somme des 10 premiers termes d'une suite arithmétique de premier terme u₀ = 2 et de raison r = 3 ?","option_a":"155","option_b":"170","option_c":"185","option_d":"200","option_e":"","option_f":"","bonne_reponse":"b","explication":"La somme des n premiers termes d'une suite arithmétique est donnée par Sₙ = n\/2 * (2u₀ + (n-1)r). Ici, S₁₀ = 10\/2 * (4 + 27) = 5 * 31 = 155.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"155\", \"b\": \"170\", \"c\": \"185\", \"d\": \"200\"}}","_debug_options_count":4},{"id":61122,"question":"Une suite définie par uₙ₊₁ = 2uₙ + 1 avec u₀ = 0 est-elle bornée ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Non, car cette suite est croissante et tend vers l'infini. Elle n'est donc pas 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":61123,"question":"Quelle est la limite de la suite uₙ = (n² + 1)\/(2n² - 3) lorsque n tend vers l'infini ?","option_a":"1\/2","option_b":"1","option_c":"0","option_d":"2","option_e":"","option_f":"","bonne_reponse":"a","explication":"En divisant numérateur et dénominateur par n², on obtient uₙ = (1 + 1\/n²)\/(2 - 3\/n²). Lorsque n tend vers l'infini, la limite est 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"1\/2\", \"b\": \"1\", \"c\": \"0\", \"d\": \"2\"}}","_debug_options_count":4},{"id":61124,"question":"Le théorème de comparaison peut-il être utilisé pour étudier la convergence d'une suite ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Oui, si une suite est encadrée par deux suites dont on connaît la convergence, on peut en déduire sa propre convergence.","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":61125,"question":"Quelle est la raison d'une suite géométrique dont les termes sont : 5, 15, 45, 135, ... ?","option_a":"2","option_b":"3","option_c":"4","option_d":"5","option_e":"","option_f":"","bonne_reponse":"b","explication":"La raison d'une suite géométrique est le rapport entre deux termes consécutifs. Ici, 15\/5 = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"2\", \"b\": \"3\", \"c\": \"4\", \"d\": \"5\"}}","_debug_options_count":4},{"id":61126,"question":"Une suite définie par uₙ = (-1)ⁿ est-elle convergente ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Non, car cette suite oscille entre -1 et 1 et n'admet pas de limite. Elle est donc 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}]