Quiz — Série suites réelles- Bac Maths- WaelDocuments.pdf

Question 1 sur 10 20:00

[{"id":2631,"question":"Soit la suite définie par \u003Cem\u003Eu\u003Csub\u003En+1\u003C\/sub\u003E = 2u\u003Csub\u003En\u003C\/sub\u003E - 1\u003C\/em\u003E et \u003Cem\u003Eu\u003Csub\u003E0\u003C\/sub\u003E = 3\u003C\/em\u003E. Que vaut \u003Cem\u003Eu\u003Csub\u003E2\u003C\/sub\u003E\u003C\/em\u003E ?","option_a":"5","option_b":"7","option_c":"9","option_d":"11","option_e":"","option_f":"","bonne_reponse":"c","explication":"On calcule \u003Cem\u003Eu\u003Csub\u003E1\u003C\/sub\u003E = 2*3 - 1 = 5\u003C\/em\u003E puis \u003Cem\u003Eu\u003Csub\u003E2\u003C\/sub\u003E = 2*5 - 1 = 9\u003C\/em\u003E.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"5\", \"b\": \"7\", \"c\": \"9\", \"d\": \"11\"}}","_debug_options_count":4},{"id":2632,"question":"Toute suite croissante est convergente.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une suite croissante peut diverger vers +∞ si 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":2633,"question":"Soit la suite \u003Cem\u003Eu\u003Csub\u003En\u003C\/sub\u003E = (-1)\u003Csup\u003En\u003C\/sup\u003E\u003C\/em\u003E. Que vaut sa limite ?","option_a":"0","option_b":"1","option_c":"-1","option_d":"La suite n'a pas de limite","option_e":"","option_f":"","bonne_reponse":"d","explication":"La suite oscille entre -1 et 1, donc elle n'a pas de limite.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"d\", \"options\": {\"a\": \"0\", \"b\": \"1\", \"c\": \"-1\", \"d\": \"La suite n'a pas de limite\"}}","_debug_options_count":4},{"id":2634,"question":"Le théorème des gendarmes s'applique à une suite \u003Cem\u003Eu\u003Csub\u003En\u003C\/sub\u003E\u003C\/em\u003E telle que \u003Cem\u003Ev\u003Csub\u003En\u003C\/sub\u003E ≤ u\u003Csub\u003En\u003C\/sub\u003E ≤ w\u003Csub\u003En\u003C\/sub\u003E\u003C\/em\u003E avec \u003Cem\u003Ev\u003Csub\u003En\u003C\/sub\u003E\u003C\/em\u003E et \u003Cem\u003Ew\u003Csub\u003En\u003C\/sub\u003E\u003C\/em\u003E convergentes vers la même limite.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le théorème des gendarmes stipule que si \u003Cem\u003Ev\u003Csub\u003En\u003C\/sub\u003E\u003C\/em\u003E et \u003Cem\u003Ew\u003Csub\u003En\u003C\/sub\u003E\u003C\/em\u003E convergent vers la même limite L, alors \u003Cem\u003Eu\u003Csub\u003En\u003C\/sub\u003E\u003C\/em\u003E converge aussi vers L.","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":2635,"question":"Soit la suite \u003Cem\u003Eu\u003Csub\u003En\u003C\/sub\u003E = n\/(n+1)\u003C\/em\u003E. Que vaut sa limite ?","option_a":"0","option_b":"1","option_c":"∞","option_d":"1\/2","option_e":"","option_f":"","bonne_reponse":"b","explication":"","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\": \"1\", \"c\": \"∞\", \"d\": \"1\/2\"}}","_debug_options_count":4},{"id":2636,"question":"Une suite bornée est toujours convergente.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une suite bornée peut ne pas converger (exemple : la suite \u003Cem\u003E(-1)\u003Csup\u003En\u003C\/sup\u003E\u003C\/em\u003E).","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":2637,"question":"Soit la suite \u003Cem\u003Eu\u003Csub\u003En\u003C\/sub\u003E = 3 + 1\/n\u003C\/em\u003E. Que vaut sa limite ?","option_a":"0","option_b":"3","option_c":"∞","option_d":"1\/3","option_e":"","option_f":"","bonne_reponse":"b","explication":"Lorsque n tend vers l'infini, \u003Cem\u003E1\/n\u003C\/em\u003E 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\": \"b\", \"options\": {\"a\": \"0\", \"b\": \"3\", \"c\": \"∞\", \"d\": \"1\/3\"}}","_debug_options_count":4},{"id":2638,"question":"Le théorème de convergence monotone s'applique à une suite décroissante et minorée.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le théorème de convergence monotone s'applique à une suite monotone (croissante ou décroissante) et 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},{"id":2639,"question":"Soit la suite \u003Cem\u003Eu\u003Csub\u003En\u003C\/sub\u003E = (n² + 1)\/n\u003C\/em\u003E. Que vaut sa limite ?","option_a":"0","option_b":"1","option_c":"∞","option_d":"n","option_e":"","option_f":"","bonne_reponse":"c","explication":"En développant, \u003Cem\u003Eu\u003Csub\u003En\u003C\/sub\u003E = n + 1\/n\u003C\/em\u003E, donc la limite est +∞.","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":2640,"question":"Une suite convergente est toujours bornée.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Si une suite converge vers une limite finie, alors elle est bornée (à partir d'un certain rang).","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}]