Quiz — السلاسل العددية 1.pdf

Question 1 sur 10 20:00

[{"id":77606,"question":"Quelle est la formule du terme général d'une suite arithmétique de premier terme u₀ et de raison r ?","option_a":"uₙ = u₀ + n","option_b":"uₙ = u₀ + n·r","option_c":"uₙ = u₀·rⁿ","option_d":"uₙ = u₀ + r","option_e":"","option_f":"","bonne_reponse":"b","explication":"La formule correcte est uₙ = u₀ + n·r, où n est le rang du terme.","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 = u₀ + n\", \"b\": \"uₙ = u₀ + n·r\", \"c\": \"uₙ = u₀·r","_debug_options_count":4},{"id":77607,"question":"Une suite géométrique de raison q = 1 est toujours convergente.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une suite géométrique de raison q = 1 est constante et donc convergente vers sa valeur constante.","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":77608,"question":"Quel est le terme général d'une suite géométrique de premier terme u₀ et de raison q ?","option_a":"uₙ = u₀ + n·q","option_b":"uₙ = u₀·qⁿ","option_c":"uₙ = u₀ + qⁿ","option_d":"uₙ = u₀·n·q","option_e":"","option_f":"","bonne_reponse":"b","explication":"La formule correcte est uₙ = u₀·qⁿ, où n est le rang du terme.","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 = u₀ + n·q\", \"b\": \"uₙ = u₀·qⁿ\", \"c\": \"uₙ = u₀ ","_debug_options_count":4},{"id":77609,"question":"Si une suite (uₙ) est croissante et majorée, alors elle est convergente.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est un théorème fondamental : toute suite croissante et majorée est 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":77610,"question":"Calculez la somme des 5 premiers termes d'une suite arithmétique de premier terme 2 et de raison 3.","option_a":"25","option_b":"30","option_c":"35","option_d":"40","option_e":"","option_f":"","bonne_reponse":"c","explication":"La somme S₅ = (5\/2)×(2×2 + (5-1)×3) = (5\/2)×(4 + 12) = (5\/2)×16 = 40.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"25\", \"b\": \"30\", \"c\": \"35\", \"d\": \"40\"}}","_debug_options_count":4},{"id":77611,"question":"Une suite (uₙ) est définie par uₙ = 3n² + 2n + 1. Quelle est la nature de cette suite ?","option_a":"Arithmétique","option_b":"Géométrique","option_c":"Quadratiques","option_d":"Exponentielle","option_e":"","option_f":"","bonne_reponse":"c","explication":"La suite est quadratique car son terme général est un polynôme de degré 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"Arithmétique\", \"b\": \"Géométrique\", \"c\": \"Quadratiques\", \"d\": \"","_debug_options_count":4},{"id":77612,"question":"Si une suite (uₙ) tend vers +∞ quand n tend vers +∞, on dit qu'elle est divergente.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une suite qui tend vers +∞ ou -∞ est divergente car elle n'a pas de limite finie.","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":77613,"question":"Calculez la limite de la suite (uₙ) définie par uₙ = (2n + 1)\/(n + 3).","option_a":"0","option_b":"1","option_c":"2","option_d":"3","option_e":"","option_f":"","bonne_reponse":"c","explication":"En divisant numérateur et dénominateur par n, on obtient uₙ = (2 + 1\/n)\/(1 + 3\/n). Quand n tend vers +∞, 1\/n et 3\/n tendent vers 0, donc la limite est 2\/1 = 2.","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\": \"2\", \"d\": \"3\"}}","_debug_options_count":4},{"id":77614,"question":"Quelle est la somme infinie d'une suite géométrique de premier terme 1 et de raison 1\/2 ?","option_a":"1","option_b":"2","option_c":"3","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"b","explication":"La somme infinie d'une suite géométrique de raison |q| \u003C 1 est S = u₀\/(1 - q) = 1\/(1 - 1\/2) = 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\", \"b\": \"2\", \"c\": \"3\", \"d\": \"∞\"}}","_debug_options_count":4},{"id":77615,"question":"Si une suite (uₙ) est définie par uₙ = (-1)ⁿ, alors elle est convergente.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La suite alterne entre -1 et 1, donc elle n'a pas de limite et 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}]