Quiz — 67b9d63ad6ea5_correction_Suite_Série_BD.pdf

Question 1 sur 10 20:00

[{"id":12088,"question":"Quelle est la raison d’une suite géométrique dont le premier terme est 2 et le troisième terme est 18 ?","option_a":"3","option_b":"2","option_c":"9","option_d":"-3","option_e":"","option_f":"","bonne_reponse":"a","explication":"La raison q vérifie u_3 = u_1 * q^2 ⇒ 18 = 2 * q^2 ⇒ q^2 = 9 ⇒ q = 3 (car q \u003E 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\": \"3\", \"b\": \"2\", \"c\": \"9\", \"d\": \"-3\"}}","_debug_options_count":4},{"id":12089,"question":"Une suite arithmétique de raison 5 a pour premier terme 10. Quel est son 10ème terme ?","option_a":"55","option_b":"45","option_c":"60","option_d":"50","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le terme général est u_n = u_0 + n*r ⇒ u_9 = 10 + 9*5 = 55.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"55\", \"b\": \"45\", \"c\": \"60\", \"d\": \"50\"}}","_debug_options_count":4},{"id":12090,"question":"La série de terme général 1\/n^2 converge-t-elle ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Oui, car c’est une série de Riemann avec α = 2 \u003E 1, donc convergente.","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":12091,"question":"Quelle est la somme des 5 premiers termes d’une suite arithmétique de premier terme 3 et de raison 2 ?","option_a":"35","option_b":"25","option_c":"40","option_d":"30","option_e":"","option_f":"","bonne_reponse":"a","explication":"S_5 = (5\/2)*(u_0 + u_4) = (5\/2)*(3 + 11) = 35.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"35\", \"b\": \"25\", \"c\": \"40\", \"d\": \"30\"}}","_debug_options_count":4},{"id":12092,"question":"La suite définie par u_n = (-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 elle oscille entre -1 et 1 sans tendre vers une limite.","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":12093,"question":"Quelle est la limite de la suite u_n = (2n + 1)\/(n + 3) quand n tend vers l’infini ?","option_a":"2","option_b":"1","option_c":"0","option_d":"3","option_e":"","option_f":"","bonne_reponse":"a","explication":"En divisant numérateur et dénominateur par n, on obtient lim (2 + 1\/n)\/(1 + 3\/n) = 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\": \"1\", \"c\": \"0\", \"d\": \"3\"}}","_debug_options_count":4},{"id":12094,"question":"Une suite géométrique de raison 0,5 et de premier terme 16 a pour somme infinie :","option_a":"32","option_b":"16","option_c":"8","option_d":"4","option_e":"","option_f":"","bonne_reponse":"a","explication":"La somme infinie est S = u_0 \/ (1 - q) = 16 \/ 0,5 = 32.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"32\", \"b\": \"16\", \"c\": \"8\", \"d\": \"4\"}}","_debug_options_count":4},{"id":12095,"question":"La suite u_n = n^2 - 5n + 6 est-elle croissante à partir d’un certain rang ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Oui, car sa dérivée (2n - 5) devient positive pour n ≥ 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":12096,"question":"Quelle est la formule du terme général d’une suite géométrique de premier terme u_0 et de raison q ?","option_a":"u_n = u_0 * q^n","option_b":"u_n = u_0 + n*q","option_c":"u_n = u_0 \/ q^n","option_d":"u_n = q * u_0^n","option_e":"","option_f":"","bonne_reponse":"a","explication":"La formule correcte est u_n = u_0 * q^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\": \"u_n = u_0 * q^n\", \"b\": \"u_n = u_0 + n*q\", \"c\": \"u_n = u_0 \/ q^n\",","_debug_options_count":4},{"id":12097,"question":"La série de terme général 1\/n diverge-t-elle ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Oui, car c’est la série harmonique qui est divergente (critère de Riemann avec α = 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}]