关于杨辉三角数阵的问题
\u6768\u8f89\u4e09\u89d2\u7684\u7279\u70b9 \u8fd9\u4e2a\u6570\u9635\u7684\u6bcf\u4e00\u884c\u7684\u5de6\u8d77\u7b2c2\u4e2a\u6570\u6709\u4ec0\u4e48\u89c4\u5f8b\u662f\u8fd9\u884c\u884c\u6570\u51cf\u4e00
\u7b2cn\u884c\u7684\u7b2c1\u4e2a\u6570\u4e3a1\uff0c\u7b2c\u4e8c\u4e2a\u6570\u4e3a1\u00d7(n-1)\uff0c\u7b2c\u4e09\u4e2a\u6570\u4e3a1\u00d7(n-1)\u00d7\uff08n-2\uff09/2\uff0c\u7b2c\u56db\u4e2a\u6570\u4e3a1\u00d7(n-1)\u00d7\uff08n-2\uff09/2\u00d7\uff08n-3\uff09/3\u2026\u4f9d\u6b64\u7c7b\u63a8
\u7b2c 1 \u884c\uff1a \u3000\u30001
\u7b2c 2 \u884c\uff1a \u3000 1 1 \u3000\u3000
\u7b2c 3 \u884c\uff1a \u30001 2 1 \u3000\u3000
\u7b2c 4 \u884c\uff1a 1 3 3 1 \u3000\u3000
\u7b2c 5 \u884c\uff1a 1 4 6 4 1
\u6768\u8f89\u4e09\u89d2\u662f\u4e00\u4e2a\u7531\u6570\u5b57\u6392\u5217\u6210\u7684\u4e09\u89d2\u5f62\u6570\u8868\uff0c\u4e00\u822c\u5f62\u5f0f\u5982\u4e0b\uff1a
1 n=0
1 1 n=1
1 2 1 n=2
1 3 3 1 n=3
1 4 6 4 1 n=4
1 5 10 10 5 1 n=5
1 6 15 20 15 6 1 n=6
\u2026\u2026
\u6b64\u6570\u5217\u4e2d\u5404\u884c\u4e2d\u7684\u6570\u5b57\u6b63\u597d\u662f\u4e8c\u9879\u5f0fa+b\u4e58\u65b9\u540e\uff0c\u5c55\u5f00\u59cb\u7ec8\u5404\u9879\u7684\u7cfb\u6570\u3002\u5982\uff1a
(a+b)^1=a^1+b^1
(a+b)^2=a^2+2ab+b^2
(a+b)^3=a^3+3a^2b+3ab^2+b^3
\u2026\u2026
(a+b)^6=a^6+6a^5b+15a^4b^2+20a^3b^3+15a^2b^4+6ab^5+b^6\uff08\u6ce8\u610f\u53d1\u73b0\u89c4\u5f8b\uff09
\u2026\u2026
=2006+2005....+2+1=2007*2006/2=2013021
1+2+3+……+n-2
=2013021
绛旓細N=(n-2)+(n-3)+(n-4)+(n-5)...+(2)+(1)=2006+2005...+2+1=2007*2006/2=2013021
绛旓細璇曢鍒嗘瀽锛氱敱棰樻剰鍙煡锛氬浘涓瘡琛岀殑绗簩涓暟鍒嗗埆涓3,6,11,18锛屸︼紝鍗 锛 锛 锛 锛屸︼紝鈭 锛 锛 锛屸︼紝 锛屸埓绱姞寰楋細 锛屸埓 .
绛旓細浜嬪疄涓婃鏁伴樀鏄鏉ㄨ緣涓夎锛屽彲浠ョ湅鍋氭槸缁勫悎鏁扮殑鎺掑垪 鎵姹傜殑鏁版槸浠2005涓暟閲屼换閫2涓笉鎺掗『搴忕殑鏂规硶绉嶆暟 鏄2005*2004/2=2009010
绛旓細绠鍗曡涓涓嬭В娉曞惂銆傜n琛岀殑鎬诲拰鏄2鐨刵-1娆℃柟锛55涓暟鍒氬ソ鍗佽锛屾诲拰涓 1+2+4+鈥︹+2^9 鍒╃敤绛夋瘮鏁板垪姹傚拰鍏紡 =2^10-1 =1024-1 =1023
绛旓細灏辨槸瑕佹眰锛1,3,6,10,15,...,杩欎竴鏁板垪鐨勭1992椤规槸澶氬皯銆傝繖涓暟鍒楃殑鐗圭偣鏄細1锛1+2锛1+2+3锛1+2+3+4锛1+2+3+4+5锛...鎵浠ワ紝绗1992椤规槸锛1+2+3+...+1992=(1+1992)*1992/2=1985028
绛旓細璇曢鍒嗘瀽锛氬洜涓虹敱涓夎褰鏁伴樀鐭ワ紝绗笁琛岀殑绗簩涓暟鍙互琛ㄧず涓 锛涚鍥涜鐨勭浜屼釜鏁板彲琛ㄧず涓 锛涚浜旇鐨勭浜屼釜鏁板彲琛ㄧず涓 .鈥.鐢辨鍙悎鎯呮帹鐞嗭紝鏍规嵁鍥惧舰绗琻琛岀殑绗簩涓暟涓 .鏁呭～ .
绛旓細1 121 1331 14641 151051 浠庣浜岃寮濮嬶紝姣忚鍔犱竴鍒楋紝闄や簡棣栧熬鐨勶紝姣忓垪鏄笂涓ゅ垪鐨勫拰銆
绛旓細鐢遍鎰忓彲寰楁瘡涓琛岄兘鎴愮瓑宸暟鍒楋紝鍒嗗埆璁惧叕宸负d1锛宒2锛宒3锛屸︼紝d32锛屸︼紝dn 锛屽垯鍏樊涓虹瓑姣旀暟鍒梴dn}锛岄氶」鍏紡涓篸n=2^n(2鐨刵娆℃柟)锛宒32=2^32锛屽洜姝ゅ彧瑕佽绠楀嚭姣忎竴琛岀涓涓暟灏卞彲浠ヤ簡锛岃绗琻琛岀涓涓暟涓篴n1(n锛1)銆傛墍浠21=a11+(a11+2^1)a31=a21+(a21+2^2)鈥︹(n-1)1=a...
绛旓細涓夎褰鏁伴樀锛屼篃鍗鏉ㄨ緣涓夎 鏉ㄨ緣涓夎褰紝鍙堢О璐惧涓夎褰紝甯曟柉鍗′笁瑙掑舰锛屾槸浜岄」寮忕郴鏁板湪涓夎褰腑鐨勪竴绉嶅嚑浣曟帓鍒 鎬ц川 1銆佹瘡琛屾暟瀛楀乏鍙冲绉帮紝鐢1寮濮嬮愭笎鍙樺ぇ锛岀劧鍚庡彉灏忥紝鍥炲埌1銆 2銆佺n琛岀殑鏁板瓧涓暟涓簄涓 3銆佺n琛屾暟瀛楀拰涓2^(n锛1)銆 4銆佹瘡涓暟瀛楃瓑浜庝笂涓琛岀殑宸﹀彸涓や釜鏁板瓧涔嬪拰銆
