鈥?strong>鈥嬧€滄瘡娆¤€冭瘯閬囧埌鏁板垪棰橈紝鏄笉鏄€绘劅瑙夊儚鍦ㄦ媶鐩茬洅锛熸槑鏄庨鐩噷鍐欑潃绛夊樊绛夋瘮锛屼絾閫氶」鍏紡姝绘椿鎲嬩笉鍑烘潵锛熲€濃€?/strong>鈥?鍒厡锛佷粖澶╁挶浠氨鐢ㄤ汉璇濇媶瑙ｇ瓑宸€佺瓑姣旈€掓帹寮忕殑閫氶」鍏紡鎺ㄥ锛?绉嶅疄鐢ㄦ妧宸у寘浣犱粠鈥滀竴鑴告嚨鈥濆埌鈥滅鐮撮鈥濓紒

涓€銆佲€?strong>鈥嬪熀纭€绡囷細绛夊樊绛夋瘮鍏紡杩樿兘杩欎箞鐢紵鈥?/strong>鈥?/h2>

鈥?strong>鈥嬧€滅瓑宸暟鍒椾笉灏辨槸鍚庨」鍑忓墠椤圭瓑浜庡叕宸悧锛熺瓑姣斾笉灏辨槸涔樹釜鍏瘮锛熲€濃€?/strong>鈥?娌￠敊锛佷絾棰樼洰寰€寰€涓嶄細鐩存帴鍛婅瘔浣犺繖浜涜寰嬶紝鑰屾槸鐢ㄩ€掓帹寮忔寲鍧戙€傛瘮濡傜湅鍒拌繖绉嶅紡瀛愶細

• 鈥?strong>鈥嬬瓑宸暟鍒楅€掓帹寮忊€?/strong>鈥嬶細a鈧?= a鈧欌倠鈧?+ d
• 鈥?strong>鈥嬬瓑姣旀暟鍒楅€掓帹寮忊€?/strong>鈥嬶細a鈧?= a鈧欌倠鈧?脳 q

杩欐椂鍊欑洿鎺ュ鐢ㄩ€氶」鍏紡灏辫锛?/p>

• 鈥?strong>鈥嬬瓑宸€氶」鈥?/strong>鈥嬶細a鈧?= a鈧?+ (n-1)d
• 鈥?strong>鈥嬬瓑姣旈€氶」鈥?/strong>鈥嬶細a鈧?= a鈧?脳 q鈦库伝鹿

鈥?strong>鈥嬩妇涓牀瀛愷煂扳€?/strong>鈥嬶細
宸茬煡绛夊樊鏁板垪{a鈧檥涓紝a鈧?2锛宎鈧?5锛屾眰a鈧佲個銆?br/> 鈥?strong>鈥嬭В娉曗€?/strong>鈥嬶細鍏堢畻鍑哄叕宸甦=5-2=3锛屽啀浠ｅ叆鍏紡锛歛鈧佲個=2+(10-1)脳3=29銆?br/> 锛堟槸涓嶆槸绠€鍗曞埌鎯冲摥锛熶絾鑰冭瘯鍙笉浼氭€诲嚭閫佸垎棰橈紒锛?/p>

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浜屻€佲€?strong>鈥嬭繘闃剁瘒锛氬綋閫掓帹寮忓紑濮嬧€滄悶浜嬫儏鈥濃€?/strong>鈥?/h2>

鈥?strong>鈥嬧€滃鏋滈€掓帹寮忛噷娣疯繘浜嗗叾浠栧榄旈鎬紝姣斿a鈧?= 2a鈧欌倠鈧?+3锛岃繕鑳界敤绛夋瘮鍏紡鍚楋紵鈥濃€?/strong>鈥?褰撶劧涓嶈锛佽繖鏃跺€欏氨瑕佷笂鈥?strong>鈥嬪緟瀹氱郴鏁版硶鈥?/strong>鈥嬩簡銆?/p>

鈥?strong>鈥嬫搷浣滃彛璇€鈥?/strong>鈥嬶細鎶婇€掓帹寮忔敼鍐欐垚绛夋瘮缁撴瀯锛?br/> 姣斿瀵逛簬a鈧?= 2a鈧欌倠鈧?+3锛?/p>

1. 鈥?strong>鈥嬪亣璁惧瓨鍦ㄥ父鏁発鈥?/strong>鈥嬶紝浣垮緱a鈧?+k = 2(a鈧欌倠鈧?+k)
2. 灞曞紑鍚庡姣斿師寮忥紝鍙戠幇k=3锛屾墍浠ユ瀯閫犳柊鏁板垪b鈧?= a鈧?+3锛屽畠婊¤冻b鈧?= 2b鈧欌倠鈧?/li>
3. 绛夋瘮鏁板垪閫氶」绉掕В锛歜鈧?= b鈧伱?鈦库伝鹿锛屾渶鍚庤繕鍘熷緱a鈧?= b鈧?-3

鈥?strong>鈥嬪叧閿偣鈥?/strong>鈥嬶細閫氳繃鈥?strong>鈥嬪紩鍏ヨ緟鍔╂暟鍒椻€?/strong>鈥嬶紝鎶婇潪绛夋瘮閫掓帹寮忓己琛屸€滄幇鈥濇垚绛夋瘮缁撴瀯銆?/p>

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涓夈€佲€?strong>鈥嬮珮闃舵妧宸э細涓冪姝﹀櫒閫愪釜鍑荤牬鈥?/strong>鈥?/h2>

1. 鈥?strong>鈥嬬疮鍔犳硶鈥斺€斿浠樼嚎鎬ч€掓帹鐨勨€滄祦姘寸嚎鈥濃€?/strong>鈥?/h3>

鈥?strong>鈥嬮€傜敤鍦烘櫙鈥?/strong>鈥嬶細閫掓帹寮忓舰濡俛鈧?= a鈧欌倠鈧?+ f(n)锛屾瘮濡俛鈧?= a鈧欌倠鈧?+2n+1銆?br/> 鈥?strong>鈥嬫搷浣滄楠も€?/strong>鈥嬶細

• 鎶妌=2鍒皀鐨勫紡瀛愬叏鍐欏嚭鏉ワ細
  a鈧?-a鈧?= f(2)
  a鈧?-a鈧?= f(3)
  鈥︹€?br/> a鈧?-a鈧欌倠鈧?= f(n)
• 鈥?strong>鈥嬫墍鏈夊紡瀛愮浉鍔犫€?/strong>鈥嬶紝涓棿椤规姷娑堬紝鍓╀笅a鈧?= a鈧?+ 危f(k)

2. 鈥?strong>鈥嬬疮涔樻硶鈥斺€斿鐞嗕箻绉瀷閫掓帹鐨勨€滃彔鍙犱箰鈥濃€?/strong>鈥?/h3>

鈥?strong>鈥嬮€傜敤鍦烘櫙鈥?/strong>鈥嬶細閫掓帹寮忓舰濡俛鈧?= a鈧欌倠鈧?脳 f(n)锛屾瘮濡俛鈧?= 3鈦?脳 a鈧欌倠鈧併€?br/> 鈥?strong>鈥嬫搷浣滄楠も€?/strong>鈥嬶細

• 鍚岀疮鍔犳硶鐨勬€濊矾锛屼絾鏀逛负鈥?strong>鈥嬭繛涔樷€?/strong>鈥嬶細
  a鈧?a鈧?= f(2)
  a鈧?a鈧?= f(3)
  鈥︹€?br/> a鈧?a鈧欌倠鈧?= f(n)
• 鈥?strong>鈥嬫墍鏈夊紡瀛愮浉涔樷€?/strong>鈥嬶紝寰梐鈧?= a鈧?脳 螤f(k)

3. 鈥?strong>鈥嬬壒寰佹牴娉曗€斺€旇В楂橀樁閫掓帹鐨勨€滀竾鑳介挜鍖欌€濃€?/strong>鈥?/h3>

鈥?strong>鈥嬮€傜敤鍦烘櫙鈥?/strong>鈥嬶細褰㈠a鈧?= pa鈧欌倠鈧?+ qa鈧欌倠鈧傜殑浜岄樁閫掓帹寮忋€?br/> 鈥?strong>鈥嬫搷浣滄楠も€?/strong>鈥嬶細

1. 鍐欏嚭鐗瑰緛鏂圭▼锛歺虏 = px + q
2. 瑙ｆ柟绋嬪緱鏍刮便€佄?/li>
3. 鏍规嵁鏍圭殑鎯呭喌鍐欓€氶」锛?
   • 鈥?strong>鈥嬩袱瀹炴牴鈥?/strong>鈥嬶細a鈧?= A伪鈦?+ B尾鈦?/li>
   • 鈥?strong>鈥嬮噸鏍光€?/strong>鈥嬶細a鈧?= (A + Bn)伪鈦?/li>

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鍥涖€佲€?strong>鈥嬬壒娈婄被鍨嬶細杩欎簺閫掓帹寮忔湁涓撳睘瑙ｆ硶鈥?/strong>鈥?/h2>

1. 鈥?strong>鈥嬪彇鍊掓暟娉曗€斺€斿垎寮忛€掓帹鐨勨€滃彉褰㈡湳鈥濃€?/strong>鈥?/h3>

鈥?strong>鈥嬮€傜敤鍦烘櫙鈥?/strong>鈥嬶細閫掓帹寮忓舰濡俛鈧?= (pa鈧欌倠鈧?+ q)/(ra鈧欌倠鈧?+ s)锛屾瘮濡俛鈧?= 2a鈧欌倠鈧?(a鈧欌倠鈧?+3)銆?br/> 鈥?strong>鈥嬫搷浣滄楠も€?/strong>鈥嬶細

• 涓よ竟鍙栧€掓暟锛屽緱鍒?/a鈧?= A(1/a鈧欌倠鈧? + B锛岃浆鍖栦负绾挎€ч€掓帹寮?/li>

2. 鈥?strong>鈥嬪彇瀵规暟娉曗€斺€旀寚鏁板瀷閫掓帹鐨勨€滈檷缁存墦鍑烩€濃€?/strong>鈥?/h3>

鈥?strong>鈥嬮€傜敤鍦烘櫙鈥?/strong>鈥嬶細閫掓帹寮忓惈鎸囨暟椤癸紝濡俛鈧?= a鈧欌倠鈧伮层€?br/> 鈥?strong>鈥嬫搷浣滄楠も€?/strong>鈥嬶細

• 涓よ竟鍙栧鏁帮紝杞寲涓虹嚎鎬ч€掓帹锛歭n a鈧?= 2 ln a鈧欌倠鈧?/li>

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浜斻€佲€?strong>鈥嬩釜浜鸿鐐癸細鍒鎶€宸х粦鏋讹紝鏍稿績鏄粨鏋勫垎鏋愨€?/strong>鈥?/h2>

寰堝浜鸿寰楁暟鍒楅毦锛屽叾瀹炴槸娌℃姄浣忊€?strong>鈥嬮€掓帹寮忕殑缁撴瀯鐗瑰緛鈥?/strong>鈥嬨€傛瘮濡傦細

• 鈥?strong>鈥嬬嚎鎬ч€掓帹鈥?/strong>鈥嬶紙a鈧欎笌a鈧欌倠鈧佹垚涓€娆″叧绯伙級鈫?浼樺厛鐢ㄥ緟瀹氱郴鏁版硶
• 鈥?strong>鈥嬪垎寮忛€掓帹鈥?/strong>鈥嬶紙a鈧欏湪鍒嗘瘝鎴栧垎瀛愶級鈫?鑰冭檻鍙栧€掓暟
• 鈥?strong>鈥嬪惈鎸囨暟鎴栦箻绉€?/strong>鈥嬧啋 鍙栧鏁版垨绱箻

鈥?strong>鈥嬭€冭瘯鍋峰垎鎶€宸р€?/strong>鈥嬶細鍏堝啓鍓?-4椤癸紝瑙傚療瑙勫緥鍐嶉€夋柟娉曪紒姣斿绠楀嚭a鈧?2锛宎鈧?5锛宎鈧?8锛屾槑鏄剧瓑宸紝鐩存帴濂楀叕寮忕渷鏃堕棿銆?/p>

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鍏€佲€?strong>鈥嬫€荤粨锛氬缁冧範锛屽皯姝昏鈥?/strong>鈥?/h2>

閫氶」鍏紡鎺ㄥ灏卞儚鈥?strong>鈥嬫惌绉湪鈥?/strong>鈥嬶紝鎺屾彙鏍稿績鏂规硶鍚庯紝90%鐨勯€掓帹寮忛兘鑳芥媶瑙ｃ€傝浣忎袱涓師鍒欙細

1. 鈥?strong>鈥嬭兘杞寲鎴愮瓑宸?绛夋瘮鐨勭粨鏋勶紝缁濅笉纭畻鈥?/strong>鈥?/li>
2. 鈥?strong>鈥嬪墠鍑犻」璁＄畻鍒伔鎳掞紝瑙勫緥寰€寰€钘忓湪杩欓噷鈥?/strong>鈥?/li>

涓嬫鍐嶉亣鍒伴€掓帹寮忥紝榛樺康涓夐亶锛氣€滅粨鏋勫垎鏋愶紒缁撴瀯鍒嗘瀽锛佺粨鏋勫垎鏋愶紒鈥?淇濅綘瑙ｉ閫熷害缈诲€嶏紒

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