10到20的平方规律，用含n的式子表示 2591420的规律用含n的式子表示
11\u7684\u5e73\u65b9\u523020\u7684\u5e73\u65b9\u6709\u89c4\u5f8b\u5417\u89c4\u5f8b\uff1a
\u5148\u8bb0\u4f4f11\u7684\u5e73\u65b9\u662f121 \u7136\u540e\u4f9d\u6b21\u63a5\u4e0b\u6765\u7684\u6570\u7684\u5e73\u65b9\u4f9d\u6b21\u589e\u52a0 23\u300125\u300127\u300129\u300131\u300133\u300135\u300137\u300139\uff0c\u5c31\u80fd\u77e5\u905311\u523020\u7684\u5e73\u65b9\u4e86\uff0c\u598211\u7684\u5e73\u65b9\u662f121+23=144 \u662f12\u7684\u5e73\u65b9 144+25=169\u662f13\u7684\u5e73\u65b9\u3002
\u6269\u5c55\u8d44\u6599\uff1a
\u5e73\u65b9\u662f\u4e00\u79cd\u8fd0\u7b97\uff0c\u6bd4\u5982\uff0ca\u7684\u5e73\u65b9\u8868\u793aa\u00d7a\uff0c\u7b80\u5199\u6210a²\uff0c\u4e5f\u53ef\u5199\u6210a\u00d7a(a\u7684\u4e00\u6b21\u65b9\u4e58a\u7684\u4e00\u6b21\u65b9\u7b49\u4e8ea\u76842\u6b21\u65b9\uff09\uff0c\u4f8b\u59824\u00d74=16\uff0c8\u00d78=64\uff0c\u5e73\u65b9\u7b26\u53f7\u4e3a2\u3002
\u76f8\u4f20\u5370\u5ea6\u6709\u4f4d\u5916\u6765\u7684\u5927\u81e3\u8ddf\u56fd\u738b\u4e0b\u68cb\uff0c\u56fd\u738b\u8f93\u4e86\uff0c\u5c31\u7b54\u5e94\u6ee1\u8db3\u4ed6\u4e00\u4e2a\u8981\u6c42\uff1a\u5728\u68cb\u76d8\u4e0a\u653e\u7c73\u7c92\u3002\u7b2c\u4e00\u683c\u653e1\u7c92\uff0c\u7b2c\u4e8c\u683c\u653e2\u7c92\uff0c\u7136\u540e\u662f4\u7c92\uff0c8\u7c92\uff0c16\u7c92\u2026\u76f4\u5230\u653e\u523064\u683c\u3002\u56fd\u738b\u54c8\u54c8\u5927\u7b11\uff0c\u8ba4\u4e3a\u4ed6\u5f88\u50bb\uff0c\u4ee5\u4e3a\u53ea\u8981\u8fd9\u4e48\u4e00\u70b9\u7c73\u3002
\u6309\u7167\u5927\u81e3\u7684\u8981\u6c42\uff0c\u653e\u6ee164\u4e2a\u683c\uff0c\u9700\u7c73 \u7c92\u3002\u8fd9\u4e2a\u6570\u662f18446744073709551615\uff0c\u662f\u4e8c\u5341\u4f4d\u7684\u6570\u5b57\u3002\u8fd9\u4e9b\u7c73\u522b\u8bf4\u503e\u7a7a\u56fd\u5e93\uff0c\u5c31\u662f\u6574\u4e2a\u5370\u5ea6\uff0c\u751a\u81f3\u5168\u4e16\u754c\u7684\u7c73\uff0c\u90fd\u65e0\u6cd5\u6ee1\u8db3\u8fd9\u4e2a\u5927\u81e3\u7684\u8981\u6c42\uff01
2=2\uff0cn=1,\u8bbe\u4e3aa1
5=2+3\uff0cn=2,\u8bbe\u4e3aa2
9=2+3+4\uff0cn=3,\u8bbe\u4e3aa3
14=2+3+4+5\uff0cn=4,\u8bbe\u4e3aa4
20=2+3+4+5+6\uff0cn=5,\u8bbe\u4e3aa5
\u90a3\u4e48\u7b2cn\u4e2a\uff0can=2+3+4+\u2026+
(n+1)=[2+(n+1)]*n/2=(n^2+3n)/2
其中n=0,1,2,3，，，，，10
（10+n）²
=100+20n+n²
例：n=7
17²=(10+7)²
=100+140+49
=289.
绛旓細10鍒20鐢10+n琛ㄧず锛屽叾涓璶=0,1,2,3锛岋紝锛10 锛10+n锛²=100+20n+n²渚嬶細n=7 17²=(10+7)²=100+140+49 =289.
绛旓細15鐨骞虫柟鏄225 20鐨勫钩鏂规槸400 10鏄5鐨2鍊,骞虫柟鍊兼槸5鐨勫钩鏂瑰4鍊嶏紙2*2锛15鏄5鐨3鍊,骞虫柟鍊兼槸5鐨勫钩鏂瑰9鍊嶏紙3*3锛20鏄5鐨4鍊,骞虫柟鍊兼槸5鐨勫钩鏂瑰16鍊嶏紙4*4锛夌敱姝ゅ彲锛氬鏋滅敳鏁版槸涔欐暟鐨刵鍊,閭ｄ箞鐢叉暟鐨勫钩鏂瑰氨鏄箼鏁扮殑骞虫柟鐨刵*n(n鐨勫钩鏂癸級鍊.
绛旓細10鍒20鐨勫钩鏂鏁版湁锛10² = 100锛11² = 121锛岋紱12² = 144 锛13² = 169 锛14² = 196 锛15² = 225锛 16² = 256锛 17² = 289 锛18² = 324锛岋紱19² = 361 锛20² = 400銆傚钩鏂规暟瀹氫箟锛氬钩鏂规暟锛堟垨绉板畬鍏ㄥ钩鏂规暟锛...
绛旓細浠庢枃绔犱腑鐨勬暟鎹彲浠ョ湅鍑锛10鍒20鐨勫钩鏂渚濇鏄100鍒400锛岃繖鏄竴涓槑鏄剧殑绛夊樊鏁板垪锛屾瘡涓暟瀛楅兘鏄墠涓涓暟瀛椾箻浠10鐨勭粨鏋溿傚钩鏂规槸涓涓暟瀛﹁繍绠楋紝绠鍗曟潵璇村氨鏄皢涓涓暟鑷箻锛屼緥濡4鐨勫钩鏂瑰氨鏄4涔樹互4锛屽啓浣4^2锛岀瓑浜16銆傚悓鏍凤紝3鐨勫钩鏂瑰氨鏄3涔樹互3锛岀瓑浜9銆傚钩鏂圭殑杩愮畻鍦ㄦ暟瀛︿腑鏈夊叾鐗瑰畾鐨勫叕寮忋傞鍏堬紝瀵逛簬...
绛旓細1= 1骞虫柟 +0 4= 2骞虫柟+0 10=3骞虫柟+1 20=4骞虫柟+4 35=5骞虫柟+10 56=6骞虫柟+20 84=7骞虫柟+35 an=n(n+1)(n+2)/6 姹傞噰绾硚~璋㈣阿锛侊紒
绛旓細1骞虫柟=0+1=1 2骞虫柟=1骞虫柟+1+2=4 3骞虫柟=2骞虫柟+2+3=9 鈥︹30骞虫柟=29骞虫柟+29+30=900 n骞虫柟=锛坣-1)骞虫柟+锛坣-1锛+n 鍦ㄨ嚜鐒舵暟鍐呴氱敤
绛旓細2n骞虫柟锛4n+4
绛旓細1鍒20鐨勫钩鏂琛ㄥ鍥炬墍绀猴細骞虫柟璁＄畻鏂规硶 a鐨勫钩鏂硅〃绀篴脳a锛岀畝鍐欐垚a²锛屼篃鍙啓鎴恆脳a(a鐨勪竴娆℃柟涔榓鐨勪竴娆℃柟绛変簬a鐨2娆℃柟锛夈備緥濡傦細4脳4=16锛8脳8=64锛屽钩鏂圭鍙蜂负²銆傞櫎浜嗕唬鏁颁腑鐨勮绠楋紝骞虫柟涔熸槸闈㈢Н鐨勫崟浣嶏紝渚嬪骞虫柟绫炽佸钩鏂瑰帢绫崇瓑銆
绛旓細10浠ュ唴锛屾槸涓綅鏁鐨勫钩鏂銆11~19锛(10+n)^2=100+20n+n^2銆21~29锛(20+n)^2=400+40n+n^2銆俷=1銆2銆併併9銆
绛旓細1鐨勫钩鏂 = 1 2鐨勫钩鏂=4 3鐨勫钩鏂=9 4鐨勫钩鏂=16 5鐨勫钩鏂=25 6鐨勫钩鏂=36 7鐨勫钩鏂=49 8鐨勫钩鏂=64 9鐨勫钩鏂=81 10鐨勫钩鏂=100 11鐨勫钩鏂=121 12鐨勫钩鏂=144 13鐨勫钩鏂=169 14鐨勫钩鏂=196 15鐨勫钩鏂=225 16鐨勫钩鏂=256 17鐨勫钩鏂=289 18鐨勫钩鏂=324 19鐨勫钩鏂=361 20鐨勫钩鏂=400 ...
