Quiz — Suites.doc

Question 1 sur 10 20:00

[{"id":47648,"question":"Quelle est la formule du terme général d'une suite arithmétique de premier terme u1 et de raison r ?","option_a":"u_n = u1 + (n-1)r","option_b":"u_n = u1 * r^(n-1)","option_c":"u_n = u1 + n*r","option_d":"u_n = u1 * (n-1)","option_e":"","option_f":"","bonne_reponse":"a","explication":"La formule du terme général d'une suite arithmétique est u_n = u1 + (n-1)r, où u1 est le premier terme et r est la raison.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"u_n = u1 + (n-1)r\", \"b\": \"u_n = u1 * r^(n-1)\", \"c\": \"u_n = u1 + n","_debug_options_count":4},{"id":47649,"question":"Une suite géométrique de raison r = 2 et de premier terme u1 = 3 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 |r| \u003E 1 est divergente. Ici, r = 2, 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":47650,"question":"Quelle est la somme des 5 premiers termes d'une suite arithmétique de premier terme u1 = 2 et de raison r = 3 ?","option_a":"35","option_b":"40","option_c":"45","option_d":"50","option_e":"","option_f":"","bonne_reponse":"b","explication":"La somme des n premiers termes d'une suite arithmétique est S_n = n\/2 * (2u1 + (n-1)r). Pour n=5, S_5 = 5\/2 * (4 + 12) = 40.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"35\", \"b\": \"40\", \"c\": \"45\", \"d\": \"50\"}}","_debug_options_count":4},{"id":47651,"question":"La suite définie par u_n = (-1)^n est-elle bornée ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La suite u_n = (-1)^n prend alternativement les valeurs -1 et 1, donc elle est bornée entre -1 et 1.","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":47652,"question":"Quelle est la limite de la suite u_n = (3n + 2) \/ (2n - 1) lorsque n tend vers l'infini ?","option_a":"1,5","option_b":"3\/2","option_c":"0","option_d":"L'infini","option_e":"","option_f":"","bonne_reponse":"b","explication":"En divisant numérateur et dénominateur par n, on obtient u_n = (3 + 2\/n) \/ (2 - 1\/n). Lorsque n tend vers l'infini, 2\/n et 1\/n tendent vers 0, donc la limite est 3\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"1,5\", \"b\": \"3\/2\", \"c\": \"0\", \"d\": \"L'infini\"}}","_debug_options_count":4},{"id":47653,"question":"Une suite dont le terme général est u_n = n^2 \/ (n + 1) est-elle majorée ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La suite u_n = n^2 \/ (n + 1) tend vers l'infini lorsque n tend vers l'infini, donc elle n'est pas majorée.","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":47654,"question":"Quelle est la raison d'une suite géométrique dont le 3ème terme est 12 et le 5ème terme est 48 ?","option_a":"2","option_b":"3","option_c":"4","option_d":"1,5","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le 3ème terme est u3 = u1 * r^2 = 12 et le 5ème terme est u5 = u1 * r^4 = 48. En divisant u5 par u3, on obtient r^2 = 4, donc r = 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\": \"2\", \"b\": \"3\", \"c\": \"4\", \"d\": \"1,5\"}}","_debug_options_count":4},{"id":47655,"question":"La suite définie par u_n = 1\/n est-elle décroissante ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La suite u_n = 1\/n est décroissante car pour tout n, u_{n+1} = 1\/(n+1) \u003C 1\/n = u_n.","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":47656,"question":"Quelle est la somme des termes d'une suite géométrique infinie de premier terme u1 = 5 et de raison r = 1\/2 ?","option_a":"10","option_b":"15","option_c":"20","option_d":"25","option_e":"","option_f":"","bonne_reponse":"b","explication":"La somme d'une suite géométrique infinie est S = u1 \/ (1 - r) = 5 \/ (1 - 0,5) = 10. Attention, ici u1 = 5, donc S = 5 \/ 0,5 = 10. La bonne réponse est 10.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"10\", \"b\": \"15\", \"c\": \"20\", \"d\": \"25\"}}","_debug_options_count":4},{"id":47657,"question":"Une suite convergente est-elle toujours bornée ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une suite convergente est toujours bornée. En effet, si une suite converge vers une limite L, alors il existe un rang N à partir duquel tous les termes sont proches de L, donc la suite est bornée.","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}]