1
鏁板垪
涓�銆佹暟鍒楃殑姒傚康
锛?/p>
1
锛夋暟鍒楀畾涔夛細鎸変竴瀹氭搴忔帓鍒楃殑涓�鍒楁暟鍙仛鏁板垪锛?/p>
鏁板垪涓殑姣忎釜鏁伴兘鍙繖涓暟鍒楃殑椤广�傝浣?/p>
n
a
锛屽湪鏁板垪绗竴涓綅缃殑椤瑰彨绗?/p>
1
椤癸紙鎴栭椤癸級
锛屽湪绗簩涓?
浣嶇疆鐨勫彨绗?/p>
2
椤癸紝鈥︹�︼紝搴忓彿涓?/p>
n
鐨勯」鍙
n
椤癸紙涔熷彨閫氶」锛夎浣?/p>
n
a
锛?/p>
鏁板垪鐨勪竴鑸舰寮忥細
1
a
锛?/p>
2
a
锛?/p>
3
a
锛屸�︹�︼紝
n
a
锛屸�︹�︼紝绠�璁颁綔
飦?/p>
飦?/p>
n
a
銆?/p>
渚嬶細鍒ゆ柇涓嬪垪鍚勭粍鍏冪礌鑳藉惁鏋勬垚鏁板垪
锛?/p>
1
锛?/p>
a, -3, -1, 1, b, 5, 7, 9;
(2)2010
骞村悇鐪佸弬鍔犻珮鑰冪殑鑰冪敓浜烘暟銆?/p>
锛?/p>
2
锛夐�氶」鍏紡鐨勫畾涔夛細濡傛灉鏁板垪
}
{
n
a
鐨勭
n
椤逛笌
n
涔嬮棿鐨勫叧绯诲彲浠ョ敤涓�涓叕寮忚〃绀猴紝閭ｄ箞杩欎釜鍏紡
灏卞彨杩欎釜鏁板垪鐨勯�氶」鍏紡銆?/p>
渚嬪锛氣憼锛?/p>
1
锛?/p>
2
锛?/p>
3
锛?/p>
4
锛?/p>
5
锛屸�?/p>
鈶★細
5
1
4
1
3
1
2
1
1
锛?/p>
锛?/p>
锛?/p>
锛?/p>
鈥?/p>
鏁板垪鈶犵殑閫氶」鍏紡鏄?/p>
n
a
=
n
锛?/p>
n
飩?/p>
7
锛?/p>
n
N
飥?/p>
飪?/p>
锛?/p>
锛?/p>
鏁板垪鈶＄殑閫氶」鍏紡鏄?/p>
n
a
=
1
n
锛?/p>
n
N
飥?/p>
飪?/p>
锛?/p>
銆?/p>
璇存槑锛?/p>
鈶?/p>
飦?/p>
飦?/p>
n
a
琛ㄧず鏁板垪锛?/p>
n
a
琛ㄧず鏁板垪涓殑绗?/p>
n
椤癸紝
n
a
=
飥?/p>
飥?/p>
f
n
琛ㄧず鏁板垪鐨勯�氶」鍏紡锛?/p>
鈶?/p>
鍚屼竴涓暟鍒楃殑閫氶」鍏紡鐨勫舰寮忎笉涓�瀹氬敮涓�銆備緥濡傦紝
n
a
=
(
1)
n
飥?/p>
=
1,
2
1
(
)
1,
2
n
k
k
Z
n
k
飥?/p>
飥?/p>
飥?/p>
飪?/p>
飪?/p>
飪?
飥?/p>
飥?/p>
飪?
锛?/p>
鈶笉鏄瘡涓暟鍒楅兘鏈夐�氶」鍏紡銆備緥濡傦紝
1
锛?/p>
1.4
锛?/p>
1.41
锛?/p>
1.414
锛屸�︹�?/p>
锛?/p>
3
锛夋暟鍒楃殑鍑芥暟鐗瑰緛涓庡浘璞¤〃绀猴細
搴忓彿锛?/p>
1 2 3 4 5 6
椤?/p>
锛?/p>
4 5 6 7 8 9
涓婇潰姣忎竴椤瑰簭鍙蜂笌杩欎竴椤圭殑瀵瑰簲鍏崇郴鍙湅鎴愭槸涓�涓簭鍙烽泦鍚堝埌鍙︿竴涓暟闆嗙殑鏄犲皠銆?/p>
浠庡嚱鏁拌鐐圭湅锛?/p>
鏁?
鍒楀疄璐ㄤ笂鏄畾涔夊煙涓烘鏁存暟闆?/p>
N
飥?/p>
锛堟垨瀹冪殑鏈夐檺瀛愰泦锛夌殑鍑芥暟
(
)
f
n
褰撹嚜鍙橀噺
n
浠?/p>
1
寮�濮嬩緷娆″彇鍊兼椂瀵瑰簲鐨勪竴
绯诲垪鍑芥暟鍊?/p>
(1),
(2),
(3),
f
f
f
鈥︹�︼紝
(
)
f
n
锛屸�︹�︼紟閫氬父鐢?/p>
n
a
鏉ヤ唬鏇?/p>
飥?/p>
飥?/p>
f
n
锛屽叾鍥捐薄鏄竴缇ゅ绔嬬偣銆?/p>
渚嬶細鐢诲嚭鏁板垪
1
2
飥?/p>
飥?/p>
n
a
n
鐨勫浘鍍?/p>
.
锛?/p>
4
锛夋暟鍒楀垎绫伙細鈶犳寜鏁板垪椤规暟鏄湁闄愯繕鏄棤闄愬垎锛氭湁绌锋暟鍒楀拰鏃犵┓鏁板垪锛涒憽鎸夋暟鍒楅」涓庨」涔嬮棿鐨勫ぇ灏?/p>
鍏崇郴鍒嗭細鍗曡皟鏁板垪锛堥�掑鏁板垪銆侀�掑噺鏁板垪锛?/p>
銆佸父鏁板垪鍜屾憜鍔ㄦ暟鍒椼�?/p>
渚嬶細涓嬪垪鐨勬暟鍒楋紝鍝簺鏄�掑鏁板垪銆侀�掑噺鏁板垪銆佸父鏁板垪銆佹憜鍔ㄦ暟鍒楋紵
锛?/p>
1
锛?/p>
1
锛?/p>
2
锛?/p>
3
锛?/p>
4
锛?/p>
5
锛?/p>
6
锛屸�?/p>
(2)10, 9, 8, 7, 6, 5,
鈥?/p>
(3) 1, 0, 1, 0, 1, 0,
鈥?/p>
(4)a, a, a, a, a,
鈥?/p>
锛?/p>
5
锛夋暟鍒?/p>
{
n
a
}
鐨勫墠
n
椤瑰拰
n
S
涓庨�氶」
n
a
鐨勫叧绯伙細
1
1
(
1)
(
2)
n
n
n
S
n
a
S
S
n
飥?/p>
飥?/p>
飪?/p>
飥?/p>
飪?/p>
飥?/p>
飪?/p>
鈮?/p>
渚嬶細宸茬煡鏁板垪
}
{
n
a
鐨勫墠
n
椤瑰拰
3
2
2
飥?/p>
飥?/p>
n
s
n
锛屾眰鏁板垪
}
{
n
a
鐨勯�氶」鍏紡
浜屻�佺瓑宸暟鍒?/p>
棰樺瀷涓�
銆佺瓑宸暟鍒楀畾涔夛細涓�鑸湴锛屽鏋滀竴涓暟鍒椾粠绗?/p>
2
椤硅捣锛屾瘡涓�椤逛笌瀹冪殑鍓嶄竴椤圭殑宸瓑浜庡悓涓�涓父鏁帮紝閭ｄ箞
杩欎釜鏁板垪灏卞彨绛夊樊鏁板垪锛岃繖涓父鏁板彨鍋氱瓑宸暟鍒楃殑鍏樊锛屽叕宸�氬父鐢ㄥ瓧姣?/p>
d
琛ㄧず銆傜敤閫掓帹鍏紡琛ㄧず涓?/p>
1
(
2)
n
n
a
a
d
n
飥?/p>
飥?/p>
飥?/p>
飩?/p>
鎴?/p>
1
(
1)
n
n
a
a
d
n
飥?/p>
飥?/p>
飥?/p>
飩?/p>
銆?/p>
渚嬶細绛夊樊鏁板垪
1
2
飥?/p>
飥?/p>
n
a
n
锛?/p>
飥?/p>
飥?/p>
飥?/p>
1
n
n
a
a
棰樺瀷浜?/p>
銆佺瓑宸暟鍒楃殑閫氶」鍏紡锛?/p>
1
(
1)
n
a
a
n
d
飥?/p>
飥?/p>
飥?/p>
锛?/p>
璇存槑锛氱瓑宸暟鍒楋紙閫氬父鍙О涓?/p>
A
P
鏁板垪锛夌殑鍗曡皟鎬э細
d
0
飥?/p>
涓洪�掑鏁板垪锛?/p>
0
d
飥?/p>
涓哄父鏁板垪锛?/p>
0
d
飥?/p>
涓洪�掑噺鏁?/p>
鍒椼�?/p>
渚嬶細
1.
宸茬煡绛夊樊鏁板垪
飦?/p>
飦?/p>
n
a
涓紝
12
4
9
7
1
16
a
a
a
a
锛屽垯
锛?/p>
飥?/p>
飥?/p>
飥?/p>
绛変簬锛?/p>
锛?/p>
A
锛?/p>
15 B
锛?/p>
30 C
锛?/p>
31 D
锛?/p>
64
2.
{
}
n
a
鏄椤?/p>
1
1
a
飥?/p>
锛屽叕宸?/p>
3
d
飥?/p>
鐨勭瓑宸暟鍒楋紝濡傛灉
2005
n
a
飥?/p>
锛屽垯搴忓彿
n
绛変簬
锛?/p>
A
锛?/p>
667
锛?/p>
B
锛?/p>
668
锛?/p>
C
锛?/p>
669
锛?/p>
D
锛?/p>
670
3.
绛夊樊鏁板垪
1
2
,
1
2
飥?/p>
飥?/p>
飥?/p>
飥?/p>
飥?/p>
n
b
n
a
n
n
锛屽垯
n
a
涓?/p>
n
b
涓?/p>
锛堝～鈥滈�掑鏁板垪鈥?/p>
鎴栤�滈�掑噺鏁板垪鈥?/p>
锛?/p>
棰樺瀷涓?/p>
銆佺瓑宸腑椤圭殑姒傚康锛?/p>
瀹氫箟锛氬鏋?/p>
a
锛?/p>
A
锛?/p>
b
鎴愮瓑宸暟鍒楋紝閭ｄ箞
A
鍙仛
a
涓?/p>
b
鐨勭瓑宸腑椤广�傚叾涓?/p>
2
a
b
A
飥?/p>
飥?/p>
a
锛?/p>
A
锛?/p>
b
鎴愮瓑宸暟鍒?/p>
飪?/p>
2
a
b
A
飥?/p>
飥?
鍗筹細
2
1
2
飥?/p>
飥?/p>
飥?/p>
飥?/p>
n
n
n
a
a
a
锛?/p>
m
n
m
n
n
a
a
a
飥?/p>
飥?/p>
飥?/p>
飥?/p>
2
锛?/p>
渚嬶細
1
锛?/p>
锛?/p>
06
鍏ㄥ浗
I
锛夎
飦?/p>
飦?/p>
n
a
鏄叕宸负姝ｆ暟鐨勭瓑宸暟鍒楋紝鑻?/p>
1
2
3
15
a
a
a
飥?/p>
飥?/p>
飥?/p>
锛?/p>
1
2
3
80
a
a
a
飥?/p>
锛屽垯
11
12
13
a
a
a
飥?/p>
飥?/p>
飥?/p>
锛?/p>
锛?/p>
A
锛?/p>
120
B
锛?/p>
105
C
锛?/p>
90
D
锛?/p>
75
2.
璁炬暟鍒?/p>
{
}
n
a
鏄崟璋冮�掑鐨勭瓑宸暟鍒楋紝鍓嶄笁椤圭殑鍜屼负
12
锛屽墠涓夐」鐨勭Н涓?/p>
48
锛屽垯瀹冪殑棣栭」鏄紙
锛?/p>
A
锛?/p>
1 B.2 C.4 D.8
棰樺瀷鍥?/p>
銆佺瓑宸暟鍒楃殑鎬ц川锛?/p>
锛?/p>
1
锛夊湪绛夊樊鏁板垪
飦?/p>
飦?/p>
n
a
涓紝浠庣
2
椤硅捣锛屾瘡涓�椤规槸瀹冪浉閭讳簩椤圭殑绛夊樊涓」锛?/p>
锛?/p>
2
锛夊湪绛夊樊鏁板垪
飦?/p>
飦?/p>
n
a
涓紝鐩搁殧绛夎窛绂荤殑椤圭粍鎴愮殑鏁板垪鏄瓑宸暟鍒楋紱
锛?/p>
3
锛夊湪绛夊樊鏁板垪
飦?/p>
飦?/p>
n
a
涓紝瀵逛换鎰?/p>
m
锛?/p>
n
N
飥?/p>
飪?/p>
锛?/p>
(
)
n
m
a
a
n
m
d
飥?/p>
飥?/p>
飥?/p>
锛?/p>
n
m
a
a
d
n
m
飥?/p>
飥?
飥?/p>
(
)
m
n
飩?/p>
锛?/p>
锛?/p>
4
锛夊湪绛夊樊鏁板垪
飦?/p>
飦?/p>
n
a
涓紝鑻?/p>
m
锛?/p>
n
锛?/p>
p
锛?/p>
q
N
飥?/p>
飪?/p>
涓?/p>
m
n
p
q
飥?/p>
飥?/p>
飥?/p>
锛屽垯
m
n
p
q
a
a
a
a
飥?/p>
飥?/p>
飥?/p>
锛?/p>