计算：100的平方-99的平方+98的平方-97的平方+……+4的平方-3的平方+2 的平方-1的
\u6c42100\u5e73\u65b9-99\u5e73\u65b9+98\u5e73\u65b9-97\u5e73\u65b9+\u2026+4\u5e73\u65b9-3\u5e73\u65b9+2\u5e73\u65b9-1\u5e73\u65b9\u7684\u7b97\u6cd5\uff1f\u539f\u5f0f=\uff08100\u5e73\u65b9-99\u5e73\u65b9\uff09+\uff0898\u5e73\u65b9-97\u5e73\u65b9\uff09+\u2026+\uff084\u5e73\u65b9-3\u5e73\u65b9\uff09+\uff082\u5e73\u65b9-1\u5e73\u65b9\uff09
=\uff08100+99\uff09\u00d7\uff08100-99\uff09+\uff0898+97\uff09\u00d7\uff0898-97\uff09+\u2026+\uff084+3\uff09\u00d7\uff084-3\uff09+\uff082+1\uff09\u00d7\uff082-1\uff09
=100+99+98+97+\u2026+2+1
=5050
\u60a8\u597d\uff0c\u5bd2\u6a31\u6696\u6696\u4e3a\u4f60\u89e3\u7b54\uff1a
100+1\u662f\u53d6\u4e00\u5927\u4e00\u5c0f\uff0c\u4e24\u5934\u6570
100\u00f72\uff0c\u662f\u4e2a\u6570
\u5982\u679c\u4f60\u8ba4\u53ef\u6211\u7684\u56de\u7b54\uff0c
\u8bf7\u53ca\u65f6\u70b9\u51fb\u3010\u91c7\u7eb3\u4e3a\u6ee1\u610f\u56de\u7b54\u3011\u6309\u94ae\uff0c\uff08\u6216\u5728\u5ba2\u6237\u7aef\u53f3\u4e0a\u89d2\u8bc4\u4ef7\u70b9\u3010\u6ee1\u610f\u3011\uff09
\u4f60\u7684\u91c7\u7eb3\uff0c
\u662f\u6211\u524d\u8fdb\u7684\u52a8\u529b! \u4e5f\u4f1a\u7ed9\u4f60\u5e26\u53bb\u8d22\u5bcc\u503c\u7684\u3002
\u5982\u6709\u4e0d\u660e\u767d\uff0c
\u53ef\u4ee5\u8ffd\u95ee\uff0c\u76f4\u5230\u5b8c\u6210\u5f04\u61c2\u6b64\u9898!
=(100+99)(100-99)(98+97)(98-97)……(4+3)(4-3)(2+1)(2-1)
=100+99+98+97……4+3+2+1
=(100+1)×100÷2
=5050
绛旓細100^2-99^2=(100+99)(100-99)=100+99 98^2-97^2=(98+97)(98-97)=98+97 ...2^2-1=(2+1)(2-1)=2+1 鎵浠ヤ负100锛99锛98锛97...2锛1锛(100+1)(99+2)...(51+50) =101*50=5050
绛旓細= 100 + 99 + 98 + 97 鈥︹ + 2 + 1 = 锛1 + 100锛壝 100 梅 2 = 101 脳 50 = 5050 骞虫柟宸叕寮忥細a ² - b ² = 锛坅 + b锛夛紙a - b锛夋槑鏁欎负鎮ㄨВ绛旓紝濡傝嫢婊℃剰,璇风偣鍑籟婊℃剰绛旀];濡傝嫢鎮ㄦ湁涓嶆弧鎰忎箣澶,璇锋寚鍑,鎴戜竴瀹氭敼姝!甯屾湜杩樻偍涓涓纭瓟澶!绁濇偍瀛︿笟杩涙!
绛旓細鐢骞虫柟宸叕寮 =(100+99)(100-99)(98+97)(98-97)鈥︹(4+3)(4-3)(2+1)(2-1)=100+99+98+97鈥︹4+3+2+1 =(100+1)脳100梅2 =5050
绛旓細100鐨勫钩鏂-99鐨勫钩鏂+98鐨勫钩鏂-97鐨勫钩鏂+96鐨勫钩鏂+95鐨勫钩鏂...+2鐨勫钩鏂-1 =(100+99)脳锛100-99锛+锛98+97锛壝楋紙98=97锛+鈥︹︼紙2+1锛壝楋紙2-1锛=100+99+98+鈥︹+2+1 =5050
绛旓細100鐨勫钩鏂鍑99鐨勫钩鏂涓轰竴缁勶紝鐢ㄥ钩鏂瑰樊鍏紡=锛100-99锛夛紙100+99锛=100+99 98鐨勫钩鏂瑰噺97鐨勫钩鏂逛负涓缁勶紝=锛98-97锛夛紙98+97锛=98+97 浠ユ绫绘帹 鏈鍚庢槸100+99+98鈥︹+2+1=5050锛堢瓑宸暟鍒楋紝1+100涓缁勶紝2+99涓缁勶紝鍏50缁勶級鏈鍚庣瓟妗5050 ...
绛旓細鐢ㄥ钩鏂瑰樊 100鐨勫钩鏂-99鐨勫钩鏂+98鐨勫钩鏂-97鐨勫钩鏂+...+2鐨勫钩鏂-1 =(100+99)(100-99)+(98+97)(98-97)+鈥︹+(2+1)(2-1)=(100+99)*1+(98+97)*1+鈥︹+(2+1)*1 =100+99+98+97+鈥︹+2+1 =(100+1)*50 =5050
绛旓細瑙ｏ細鍘熷紡=锛100²-1²锛+锛2²-99²锛+锛98²-3²锛+锛4²-97²锛+...=101脳99-101脳97+101脳95-101脳93+...=101脳[锛99+95+91+...3锛-锛97+93+89+...+1锛塢=101脳锝涳紙3+99锛壝梉锛99-3锛壝4+1]梅2-[锛97+1锛夛紙97-1锛...
绛旓細瑙ｏ細鍘熷紡=(100-99)(100+99)+(98-87)(98+97)+路路路+(2-1)(2+1)=100+99+98+97+路路路+2+1 =(100+1)脳100梅2 =5050 鍒╃敤骞虫柟宸叕寮 鏈涢噰绾
绛旓細浣犲ソ锛岃繖鏄竴涓浐瀹氱殑鍏紡锛屼富瑕佽浣忚繖涓叕寮忥紝閬囧埌杩欑被鐨勯鐩洿鎺ュ鐢ㄨ繖涓叕寮忓氨鍙互绠渚跨殑璁＄畻銆傚叕寮忓涓嬶細a^2-b^2=锛坅+b锛夛紙a-b锛
绛旓細鍘熷紡=锛100骞虫柟-99骞虫柟锛+锛98骞虫柟-97骞虫柟锛+鈥+锛4骞虫柟-3骞虫柟锛+锛2骞虫柟-1骞虫柟锛=锛100+99锛壝楋紙100-99锛+锛98+97锛壝楋紙98-97锛+鈥+锛4+3锛壝楋紙4-3锛+锛2+1锛壝楋紙2-1锛=100+99+98+97+鈥+2+1 =5050 鍙傝冭祫鏂锛氬钩鏂宸叕寮 ...
