{"id":21724,"date":"2021-12-17T16:31:32","date_gmt":"2021-12-17T09:31:32","guid":{"rendered":"https:\/\/www.vietlearn.org\/post\/?p=21724"},"modified":"2021-12-17T16:31:34","modified_gmt":"2021-12-17T09:31:34","slug":"day-so","status":"publish","type":"post","link":"https:\/\/www.vietlearn.org\/kien-thuc\/day-so\/","title":{"rendered":"D\u00c3Y S\u1ed0"},"content":{"rendered":"

<\/a>A \u2013 L\u00dd THUY\u1ebeT T\u00d3M T\u1eaeT<\/strong><\/h1>\n

1. Ph\u01b0\u01a1ng ph\u00e1p quy n\u1ea1p to\u00e1n h\u1ecdc<\/strong><\/p>\n

\u0110\u1ec3 ch\u1ee9ng minh m\u1ec7nh \u0111\u1ec1 ch\u1ee9a bi\u1ebfn A(n) l\u00e0 m\u1ed9t m\u1ec7nh \u0111\u1ec1 \u0111\u00fang v\u1edbi m\u1ecdi gi\u00e1 tr\u1ecb nguy\u00ean d\u01b0\u01a1ng n, ta th\u1ef1c hi\u1ec7n nh\u01b0 sau:<\/p>\n

\u00b7 B\u01b0\u1edbc 1: Ki\u1ec3m tra m\u1ec7nh \u0111\u1ec1 \u0111\u00fang v\u1edbi n = 1.<\/p>\n

\u00b7 B\u01b0\u1edbc 2: Gi\u1ea3 thi\u1ebft m\u1ec7nh \u0111\u1ec1 \u0111\u00fang v\u1edbi s\u1ed1 nguy\u00ean d\u01b0\u01a1ng n = k tu\u1ef3 \u00fd (k \u00b3 1), ch\u1ee9ng minh r\u1eb1ng m\u1ec7nh \u0111\u1ec1 \u0111\u00fang v\u1edbi n = k + 1.<\/p>\n

Ch\u00fa \u00fd:<\/strong> N\u1ebfu ph\u1ea3i ch\u1ee9ng minh m\u1ec7nh \u0111\u1ec1 A(n) l\u00e0 \u0111\u00fang v\u1edbi v\u1edbi m\u1ecdi s\u1ed1 nguy\u00ean d\u01b0\u01a1ng n \u00b3 p th\u00ec:<\/p>\n

+ \u1ede b\u01b0\u1edbc 1, ta ph\u1ea3i ki\u1ec3m tra m\u1ec7nh \u0111\u1ec1 \u0111\u00fang v\u1edbi n = p;<\/p>\n

+ \u1ede b\u01b0\u1edbc 2, ta gi\u1ea3 thi\u1ebft m\u1ec7nh \u0111\u1ec1 \u0111\u00fang v\u1edbi s\u1ed1 nguy\u00ean d\u01b0\u01a1ng b\u1ea5t k\u00ec n = k \u00b3 p v\u00e0 ph\u1ea3i ch\u1ee9ng minh m\u1ec7nh \u0111\u1ec1 \u0111\u00fang v\u1edbi n = k + 1.<\/p>\n

2. D\u00e3y s\u1ed1<\/strong><\/p>\n

\"IMG_256\" D\u1ea1ng khai tri\u1ec3n: (un<\/sub>) = u1<\/sub>, u2<\/sub>, \u2026, un<\/sub>, \u2026<\/p>\n

3. D\u00e3y s\u1ed1 t\u0103ng, d\u00e3y s\u1ed1 gi\u1ea3m<\/strong><\/p>\n

\u00b7 (un<\/sub>) l\u00e0 d\u00e3y s\u1ed1 t\u0103ng \u00db un+1<\/sub> > un<\/sub> v\u1edbi ” n \u00ce N*.<\/p>\n

\u00db un+1<\/sub> \u2013 un<\/sub> > 0 v\u1edbi ” n \u00ce N* \u00db \"IMG_257\" v\u1edbi “n \u00ce N* ( un<\/sub> > 0).<\/p>\n

\u00b7 (un<\/sub>) l\u00e0 d\u00e3y s\u1ed1 gi\u1ea3m \u00db un+1<\/sub> < un<\/sub> v\u1edbi “n \u00ce N*.<\/p>\n

\u00db un+1<\/sub> \u2013 un<\/sub>< 0 v\u1edbi ” n \u00ce N* \u00db \"IMG_258\" v\u1edbi “n \u00ce N* (un<\/sub> > 0).<\/p>\n

4. D\u00e3y s\u1ed1 b\u1ecb ch\u1eb7n<\/strong><\/p>\n

\u00b7 (un<\/sub>) l\u00e0 d\u00e3y s\u1ed1 b\u1ecb ch\u1eb7n tr\u00ean \u00db $M \u00ce R: un<\/sub> \u00a3 M, “n \u00ce N*.<\/p>\n

\u00b7 (un<\/sub>) l\u00e0 d\u00e3y s\u1ed1 b\u1ecb ch\u1eb7n d\u01b0\u1edbi \u00db $m \u00ce R: un<\/sub> \u00b3 m, “n \u00ce N*.<\/p>\n

\u00b7 (un<\/sub>) l\u00e0 d\u00e3y s\u1ed1 b\u1ecb ch\u1eb7n \u00db $m, M \u00ce R: m \u00a3 un<\/sub> \u00a3 M, “n \u00ce N*.<\/p>\n

<\/a>B \u2013 B\u00c0I T\u1eacP<\/strong><\/h1>\n

<\/a>D\u1ea0NG 1: S\u1ed0 H\u1ea0NG C\u1ee6A D\u00c3Y S\u1ed0<\/strong><\/h2>\n

C\u00e2u 1: <\/strong>Cho d\u00e3y s\u1ed1 c\u00f3 4 s\u1ed1 h\u1ea1ng \u0111\u1ea7u l\u00e0: \"IMG_259\" . H\u00e3y t\u00ecm m\u1ed9t quy lu\u1eadt c\u1ee7a d\u00e3y s\u1ed1 tr\u00ean v\u00e0 vi\u1ebft s\u1ed1 h\u1ea1ng th\u1ee9 10 c\u1ee7a d\u00e3y v\u1edbi quy lu\u1eadt v\u1eeba t\u00ecm.<\/p>\n

A. <\/strong> \"IMG_260\" B. <\/strong> \"IMG_261\" C. <\/strong> \"IMG_262\" D. <\/strong> \"IMG_263\"<\/p>\n

C\u00e2u 2: <\/strong>Cho d\u00e3y s\u1ed1 \"IMG_264\" v\u1edbi \"IMG_265\" (a: h\u1eb1ng s\u1ed1). \"IMG_266\" l\u00e0 s\u1ed1 h\u1ea1ng n\u00e0o sau \u0111\u00e2y?<\/p>\n

A. <\/strong> \"IMG_267\" . B. <\/strong> \"IMG_268\" . C. <\/strong> \"IMG_269\" . D. <\/strong> \"IMG_270\" .<\/p>\n

C\u00e2u 3: <\/strong>Cho d\u00e3y s\u1ed1 c\u00f3 c\u00e1c s\u1ed1 h\u1ea1ng \u0111\u1ea7u l\u00e0: \"IMG_271\" S\u1ed1 h\u1ea1ng t\u1ed5ng qu\u00e1t c\u1ee7a d\u00e3y s\u1ed1 n\u00e0y l\u00e0:<\/p>\n

A. <\/strong> \"IMG_272\" . B. <\/strong> \"IMG_273\" . C. <\/strong> \"IMG_274\" . D. <\/strong> \"IMG_275\" .<\/p>\n

C\u00e2u 4: <\/strong>Cho d\u00e3y s\u1ed1 c\u00f3 c\u00e1c s\u1ed1 h\u1ea1ng \u0111\u1ea7u l\u00e0: \"IMG_276\" .S\u1ed1 h\u1ea1ng t\u1ed5ng qu\u00e1t c\u1ee7a d\u00e3y s\u1ed1 n\u00e0y l\u00e0:<\/p>\n

A. <\/strong> \"IMG_277\" . B. <\/strong> \"IMG_278\" .<\/p>\n

C. <\/strong> \"IMG_279\" . D. <\/strong> \"IMG_280\" : Kh\u00f4ng vi\u1ebft \u0111\u01b0\u1ee3c d\u01b0\u1edbi d\u1ea1ng c\u00f4ng th\u1ee9c.<\/p>\n

C\u00e2u 5: <\/strong>Cho d\u00e3y s\u1ed1 c\u00f3 c\u00e1c s\u1ed1 h\u1ea1ng \u0111\u1ea7u l\u00e0: \"IMG_281\" .S\u1ed1 h\u1ea1ng t\u1ed5ng qu\u00e1t c\u1ee7a d\u00e3y s\u1ed1 n\u00e0y l\u00e0:<\/p>\n

A. <\/strong> \"IMG_282\" . B. <\/strong> \"IMG_283\" . C. <\/strong> \"IMG_284\" . D. <\/strong> \"IMG_285\" .<\/p>\n

C\u00e2u 6: <\/strong>Cho d\u00e3y s\u1ed1 c\u00f3 c\u00e1c s\u1ed1 h\u1ea1ng \u0111\u1ea7u l\u00e0: \"IMG_286\" . S\u1ed1 h\u1ea1ng t\u1ed5ng qu\u00e1t c\u1ee7a d\u00e3y s\u1ed1 n\u00e0y c\u00f3 d\u1ea1ng?<\/p>\n

A. <\/strong> \"IMG_287\" . B. <\/strong> \"IMG_288\" . C. <\/strong> \"IMG_289\" . D. <\/strong> \"IMG_290\" .<\/p>\n

C\u00e2u 7: <\/strong>Cho d\u00e3y s\u1ed1 c\u00f3 c\u00e1c s\u1ed1 h\u1ea1ng \u0111\u1ea7u l\u00e0: \"IMG_291\" .S\u1ed1 h\u1ea1ng t\u1ed5ng qu\u00e1t c\u1ee7a d\u00e3y s\u1ed1 n\u00e0y c\u00f3 d\u1ea1ng<\/p>\n

A. <\/strong> \"IMG_292\" . B. <\/strong> \"IMG_293\" . C. <\/strong> \"IMG_294\" . D. <\/strong> \"IMG_295\".<\/strong><\/p>\n

C\u00e2u 8: <\/strong>Cho d\u00e3y s\u1ed1 c\u00f3 c\u00e1c s\u1ed1 h\u1ea1ng \u0111\u1ea7u l\u00e0: \"IMG_296\" .S\u1ed1 h\u1ea1ng t\u1ed5ng qu\u00e1t c\u1ee7a d\u00e3y s\u1ed1 n\u00e0y c\u00f3 d\u1ea1ng?<\/p>\n

A. <\/strong> \"IMG_297\" . B. <\/strong> \"IMG_298\" .<\/p>\n

C. <\/strong> \"IMG_299\" . D. <\/strong> \"IMG_300\" .<\/p>\n

C\u00e2u 9: <\/strong> Cho d\u00e3y s\u1ed1 c\u00f3 c\u00e1c s\u1ed1 h\u1ea1ng \u0111\u1ea7u l\u00e0: \"IMG_301\" \u2026.S\u1ed1 h\u1ea1ng t\u1ed5ng qu\u00e1t c\u1ee7a d\u00e3y s\u1ed1 n\u00e0y l\u00e0?<\/p>\n

A. <\/strong> \"IMG_302\" . B. <\/strong> \"IMG_303\" . C. <\/strong> \"IMG_304\" . D. <\/strong> \"IMG_305\" .<\/p>\n

C\u00e2u 10: <\/strong>Cho d\u00e3y s\u1ed1 \"IMG_306\" v\u1edbi \"IMG_307\" .S\u1ed1 h\u1ea1ng t\u1ed5ng qu\u00e1t \"IMG_308\" c\u1ee7a d\u00e3y s\u1ed1 l\u00e0 s\u1ed1 h\u1ea1ng n\u00e0o d\u01b0\u1edbi \u0111\u00e2y?<\/p>\n

A. <\/strong> \"IMG_309\" . B. <\/strong> \"IMG_310\" .<\/p>\n

C. <\/strong> \"IMG_311\" . D. <\/strong> \"IMG_312\" .<\/p>\n","protected":false},"excerpt":{"rendered":"

A \u2013 L\u00dd THUY\u1ebeT T\u00d3M T\u1eaeT 1. Ph\u01b0\u01a1ng ph\u00e1p quy n\u1ea1p to\u00e1n h\u1ecdc \u0110\u1ec3 ch\u1ee9ng minh m\u1ec7nh \u0111\u1ec1 ch\u1ee9a bi\u1ebfn A(n) l\u00e0 m\u1ed9t m\u1ec7nh \u0111\u1ec1 \u0111\u00fang v\u1edbi m\u1ecdi gi\u00e1 tr\u1ecb nguy\u00ean d\u01b0\u01a1ng n, ta th\u1ef1c hi\u1ec7n nh\u01b0 sau: \u00b7 B\u01b0\u1edbc 1: Ki\u1ec3m tra m\u1ec7nh \u0111\u1ec1 \u0111\u00fang v\u1edbi n = 1. \u00b7 B\u01b0\u1edbc 2: Gi\u1ea3 thi\u1ebft […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_disable_autopaging":false},"categories":[42],"tags":[],"class_list":["post-21724","post","type-post","status-publish","format-standard","hentry","category-toan-lop-11"],"_links":{"self":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/21724","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/comments?post=21724"}],"version-history":[{"count":1,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/21724\/revisions"}],"predecessor-version":[{"id":21782,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/21724\/revisions\/21782"}],"wp:attachment":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/media?parent=21724"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/categories?post=21724"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/tags?post=21724"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}