绮惧績鏁寸悊
绮惧績鏁寸悊
鐭ヨ瘑妗嗘灦
鎺屾彙浜嗘暟鍒楃殑鍩烘湰鐭ヨ瘑锛岀壒鍒槸绛夊樊銆佺瓑
姣旀暟鍒楃殑瀹氫箟銆侀�氶」鍏紡銆佹眰鍜屽叕寮忓強鎬ц川锛?/p>
鎺屾彙浜嗗吀鍨嬮鍨嬬殑瑙ｆ硶鍜屾暟瀛︽�濇兂娉曠殑搴旂敤锛?/p>
灏辨湁鍙兘鍦ㄩ珮鑰冧腑椤哄埄鍦拌В鍐虫暟鍒楅棶棰樸�?/p>
涓�銆佸吀鍨嬮鐨勬妧宸цВ娉?/p>
1
銆佹眰閫氶」鍏紡
锛?/p>
1
锛夎瀵熸硶銆?/p>
锛?/p>
2
锛夌敱閫掓帹鍏紡姹傞�氶」銆?/p>
瀵逛簬鐢遍�掓帹鍏紡鎵�纭畾鐨勬暟鍒楃殑姹傝В锛岄�氬父
鍙�氳繃瀵归�掓帹鍏紡鐨勫彉鎹㈣浆鍖栨垚绛夊樊鏁板垪鎴?/p>
绛夋瘮鏁板垪闂銆?/p>
(1)
閫掓帹寮忎负
a
n+1
=a
n
+d
鍙?/p>
a
n+1
=qa
n
锛?/p>
d
锛?
q
涓哄父鏁帮級
渚?/p>
1
銆?/p>
?
宸茬煡
{a
n
}
婊¤冻
a
n+1
=a
n
+2
锛岃�屼笖
a
1
=1
銆傛眰
a
n
銆?/p>
渚?/p>
1
銆佽В
?
鈭?/p>
a
n+1
-a
n
=2
涓哄父鏁扳埓
{a
n
}
鏄椤逛负
1
锛屽叕宸负
2
鐨勭瓑宸暟鍒?/p>
鈭?/p>
a
n
=1+2
锛?/p>
n-1
锛夊嵆
a
n
=2n-1
渚?/p>
2
銆佸凡鐭?/p>
{
}
n
a
婊¤冻
1
1
2
n
n
a
a
飥?/p>
飥?/p>
锛岃�?/p>
1
2
a
飥?/p>
锛屾眰
n
a
=
锛?/p>
锛?/p>
2
锛夐�掓帹寮忎负
a
n+1
=a
n
+f
锛?/p>
n
锛?/p>
渚?/p>
3
銆?/p>
宸茬煡
{
}
n
a
涓?/p>
1
1
2
a
飥?/p>
锛?/p>
1
2
1
4
1
n
n
a
a
n
飥?/p>
飥?/p>
飥?/p>
飥?/p>
锛?
姹?/p>
n
a
.
瑙?
锛?
鐢?
宸?
鐭?
鍙?
鐭?
)
1
2
)(
1
2
(
1
1
飥?/p>
飥?/p>
飥?
飥?/p>
飥?/p>
n
n
a
a
n
n
)
1
2
1
1
2
1
(
2
1
飥?/p>
飥?/p>
飥?/p>
飥?/p>
n
n
浠?/p>
n=1
锛?/p>
2
锛屸�︼紝
锛?/p>
n-1
锛?/p>
锛屼唬鍏ュ緱锛?/p>
n-1
锛変釜绛?
寮忕疮鍔狅紝鍗筹紙
a
2
-a
1
锛?/p>
+
锛?/p>
a
3
-a
2
锛?/p>
+
鈥?/p>
+
锛?/p>
a
n
-a
n-1
锛?/p>
鈽?/p>
璇存槑
?
鍙鍜?/p>
f
锛?/p>
1
锛?/p>
+f
锛?/p>
2
锛?/p>
+
鈥?/p>
+f
锛?/p>
n-1
锛?/p>
鏄彲姹傜殑锛?/p>
灏卞彲浠ョ敱
a
n+1
=a
n
+f
锛?/p>
n
锛?/p>
浠?/p>
n=1
锛?/p>
2
锛屸�︼紝
锛?/p>
n-1
锛変唬鍏ワ紝鍙緱
n-1
涓瓑寮忕疮鍔犺�屾眰
a
n
銆?/p>
(3)
閫掓帹寮忎负
a
n+1
=pa
n
+q
锛?/p>
p
锛?/p>
q
涓哄父鏁帮級
渚?/p>
4
銆?/p>
{
}
n
a
涓紝
1
1
a
飥?/p>
锛屽浜?/p>
n
锛?/p>
1
锛?/p>
n
鈭?/p>
N
锛夋湁
1
3
2
n
n
a
a
飥?/p>
飥?/p>
飥?/p>
锛屾眰
n
a
.
瑙?/p>
娉?/p>
涓�
锛?/p>
鐢?/p>
宸?/p>
鐭?/p>
閫?/p>
鎺?/p>
寮?/p>
寰?/p>
a
n+1
=3a
n
+2
锛?
a
n
=3a
n-1
+2
銆備袱寮忕浉鍑忥細
a
n+1
-a
n
=3
锛?/p>
a
n
-a
n-1
锛?/p>
鍥犳鏁板垪
{a
n+1
-a
n
}
鏄叕姣斾负
3
鐨勭瓑姣旀暟
鍒楋紝鍏堕椤逛负
a
2
-a
1
=
锛?/p>
3
脳
1+2
锛?/p>
-1=4
鈭?/p>
a
n+1
-a
n
=4
路
3
n-1
鈭?/p>
a
n+1
=3a
n
+2?
鈭?/p>
3a
n
+2-a
n
=4
路
3
n-1
鍗?/p>
a
n
=2
路
3
n-1
-1
瑙ｆ硶浜岋細
涓婃硶寰?/p>
{a
n+1
-a
n
}
鏄叕姣斾负
3
鐨勭瓑姣?/p>
鏁?/p>
鍒?/p>
锛?/p>
浜?/p>
鏄?/p>
鏈?/p>
锛?/p>
a
2
-a
1
=4
锛?/p>
a
3
-a
2
=4
路
3
锛?/p>
a
4
-a
3
=4
路
3
2
锛屸�︼紝
a
n
-a
n-1
=4
路
3
n-2
锛?/p>
鎶?/p>
n-1
涓瓑寮忕疮鍔犲緱锛氣埓
an=2
路
3n-1-1
(4)
閫掓帹寮忎负
a
n+1
=pa
n
+qn
锛?/p>
p
锛?/p>
q
涓哄父鏁帮級
)
(
3
2
1
1
飥?/p>
飥?/p>
飥?/p>
飥?/p>
飥?/p>
n
n
n
n
b
b
b
b
鐢变笂棰樼殑瑙ｆ硶锛?
寰?/p>
锛?/p>
n
n
b
)
3
2
(
2
3
飥?/p>
飥?/p>
鈭?/p>
n
n
n
n
n
b
a
)
3
1
(
2
)
2
1
(
3
2
飥?/p>
飥?/p>
飥?
(5)
閫掓帹寮忎负
2
1
n
n
n
a
pa
qa
飥?/p>
飥?/p>
飥?/p>
飥?/p>
鎬濊矾锛?/p>
璁?/p>
2
1
n
n
n
a
pa
qa
飥?/p>
飥?/p>
飥?/p>
飥?/p>
,
鍙互鍙樺舰涓猴細
2
1
1
(
)
n
n
n
n
a
a
a
a
飦?/p>
飦?/p>
飦?/p>
飥?/p>
飥?/p>
飥?/p>
飥?/p>
飥?/p>
飥?/p>
锛?/p>
鎯?
浜庢槸
{a
n+1
-
伪
a
n
}
鏄叕姣斾负尾鐨勭瓑姣旀暟
鍒楋紝灏辫浆鍖栦负鍓嶉潰鐨勭被鍨嬨�?/p>
姹?/p>
n
a
銆?/p>
(6)
閫掓帹寮忎负
S
n
涓?/p>
a
n
鐨勫叧绯诲紡
绯伙紱
锛?/p>
2
锛夎瘯鐢?/p>
n
琛ㄧず
a
n
銆?/p>
鈭?/p>
)
2
1
2
1
(
)
(
1
2
1
1
飥?/p>
飥?/p>
飥?/p>
飥?/p>
飥?
飥?/p>
飥?/p>
飥?/p>
飥?/p>
n
n
n
n
n
n
a
a
S
S
鈭?
1
1
1
2
1
飥?/p>
飥?/p>
飥?/p>
飥?
飥?/p>
飥?/p>
n
n
n
n
a
a
a
鈭?/p>
n
n
n
a
a
2
1
2
1
1
飥?/p>
飥?
飥?/p>
涓婂紡涓よ竟鍚屼箻浠?/p>
2
n+1
寰?/p>
2
n+1
a
n+1
=2
n
a
n
+2
鍒?/p>
{2
n
a
n
}
鏄叕宸负
2
鐨勭瓑宸暟鍒椼�?/p>
鈭?/p>
2
n
a
n
=2+
锛?/p>
n-1
锛?/p>
路
2=2n
鏁板垪姹傚拰鐨勫父鐢ㄦ柟娉曪細
1
銆?/p>
鎷嗛」鍒嗙粍娉?/p>
锛氬嵆鎶婃瘡涓�椤规媶鎴愬嚑椤癸紝
閲嶆柊缁勫悎鍒嗘垚鍑犵粍锛?/p>
杞寲涓虹壒娈婃暟鍒楁眰鍜屻�?/p>