将正整数按如图所示的规律排列下去,若用有序数对（n,m）表示第n排，从左到右第m个数，如（4,3）表示实数9
\u5c06\u6b63\u6574\u6570\u6309\u5982\u56fe\u6240\u793a\u7684\u89c4\u5f8b\u6392\u5217\u4e0b\u53bb\uff0e\u82e5\u7528\u6709\u5e8f\u6570\u5bf9\uff08n\uff0cm\uff09\u8868\u793a\u7b2cn\u6392\uff0c\u4ece\u5de6\u5230\u53f3\u7b2cm\u4e2a\u6570\uff0c\u5982\uff084\uff0c3\uff09\u8868\u793a\u6574\u82e5\u7528\u6709\u5e8f\u6570\u5bf9\uff08m\uff0cn\uff09\u8868\u793a\u4ece\u4e0a\u5230\u4e0b\u7b2cm\u6392\uff0c\u4ece\u5de6\u5230\u53f3\u7b2cn\u4e2a\u6570\uff0c\u5bf9\u5982\u56fe\u4e2d\u7ed9\u51fa\u7684\u6709\u5e8f\u6570\u5bf9\u548c\uff084\uff0c3\uff09\u8868\u793a\u6574\u65709\u53ef\u5f97\uff0c\uff084\uff0c3\uff09=4\u00d7(4?1)2+3=9\uff1b\uff083\uff0c1\uff09=3\u00d7(3?1)2+1=4\uff1b\u2026\uff0c\u7531\u6b64\u53ef\u4ee5\u53d1\u73b0\uff0c\u5bf9\u6240\u6709\u6570\u5bf9\uff08m\uff0cn\uff09\u3010n\u2264m\u3011\u6709\uff1a\uff08m\uff0cn\uff09=\uff081+2+3+\u2026+m-1\uff09+n=m(m?1)2+n\uff0e\u6240\u4ee5\uff0c\uff0817\uff0c2\uff09=17\u00d7(17?1)2+2=136+2=138\uff0e\u6545\u7b54\u6848\u4e3a\uff1a138\uff0e
\u4ece\u56fe\u4e2d\u53ef\u4ee5\u53d1\u89c2\uff0c\u7b2cn\u6392\u7684\u6700\u540e\u7684\u6570\u4e3a\uff1a12n\uff08n+1\uff09\u2235\u7b2c9\u6392\u6700\u540e\u7684\u6570\u4e3a\uff1a12\u00d79\uff089+1\uff09=45\uff0c\u2234\uff0810\uff0c3\uff09\u8868\u793a\u7b2c10\u6392\u7b2c3\u4e2a\u6570\uff0c\u5219\u7b2c10\u6392\u7b2c3\u4e2a\u6570\u4e3a45+3=48\uff0e\u6545\u9009\uff1aC\uff0e
第n排，(n²-n+2)/2第n排第m数，(n²-n+2)/2+(m-1).
(29,4)，表示：第29排第4数，n=29, m=4, 代入(n²-n+2)/2+(m-1)=407+3=410.
（29,4）表示的数是：410.
第64排，60个
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绛旓細浠庡浘涓彲浠ュ彂瑙傦紝绗琻鎺掔殑鏈鍚庣殑鏁颁负锛 1 2 n锛坣+1锛夆埖绗6鎺掓渶鍚庣殑鏁颁负锛 1 2 脳6锛6+1锛=21锛屸埓锛7锛2锛夎〃绀虹7鎺掔2涓暟锛屽垯绗7鎺掔浜屼釜鏁颁负21+2=23锛庢晠绛旀濉細23锛
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绛旓細绗琻鎺掞紝(n²-n+2)/2 绗琻鎺掔m鏁帮紝(n²-n+2)/2+(m-1).(29,4)锛岃〃绀猴細绗29鎺掔4鏁帮紝n=29, m=4, 浠ｅ叆(n²-n+2)/2+(m-1)=407+3=410.锛29,4锛夎〃绀虹殑鏁版槸锛410.
