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的平方
100\u5e73\u65b9-99\u5e73\u65b9+98\u5e73\u65b9-97\u5e73\u65b9+\u2026\u2026+4\u5e73\u65b9-3\u5e73\u65b9+2\u5e73\u65b9-1\u4e3a\u4ec0\u4e48\u4ed6\u7684\u7b54\u6848\u7b49\u4e8e1+2\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!
\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
=100+99+98+97+···+2+1
=(100+1)×100÷2
=5050
利用平方差公式
望采纳
答：平方差公式的应用
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的平方
=(100-99)*(100+99)+(98-97)*(98+97)+.....+(2-1)*(2+1)
=100+99+98+97+....+2+1
=(100+1)*100/2
=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鐨勫钩鏂 =锛100²-99²锛+锛98²-97²锛+锛岋紝锛+锛2²-1²锛=(100-99)(100+99)+(98-97)(98+97)+...+(2-1)(2+1)=(100+99+...+2+1)=(1+1...
绛旓細=锛100+99锛夛紙100-99锛+98^2=199+98^2=9803
绛旓細浣跨敤骞虫柟宸叕寮忥細涓や釜鏁扮殑鍜屼笌杩欎袱涓暟鐨勫樊鐨勭Н绛変簬杩欎袱涓暟鐨勫钩鏂瑰樊 100^2-99^2=锛100+99锛*锛100-99锛=199 98^2-97^2=锛98+97锛*锛98-97锛=195
绛旓細=(100 99)(100-99)=199*1=199
绛旓細棣栧厛100^2-99^2=(100+99)*(100-99)=100+99 鍚岀悊98^2-97^2=98+97 鎵浠ュ師鏉ョ殑寮忓瓙鍙互鍖栨垚= (100鐨勫钩鏂-99鐨勫钩鏂)+(98鐨勫钩鏂-97鐨勫钩鏂)+鈥+(4鐨勫钩鏂-3鐨勫钩鏂)+(2鐨勫钩鏂-1鐨勫钩鏂)=100+99+98+97+鈥︹4+3+2+1=101*50=5050 ...
绛旓細100鐨勫钩鏂-99鐨勫钩鏂+98鐨勫钩鏂-97鐨勫钩鏂光+2鐨勫钩鏂-1鐨勫钩鏂 =(100+99锛夛紙100-99锛+锛98+97锛夛紙98-97锛+鈥︹+锛4+3锛夛紙4-3锛+锛2+1锛夛紙2-1锛=100+99+98+97+96+95+鈥︹+4+3+2+1 =锛100+1锛壝100梅2 =5050
绛旓細100骞虫柟-99骞虫柟=锛100+99锛壝楋紙100-99锛夋墍浠100骞虫柟-99骞虫柟=199+1 浠ユ绫绘帹100鐨勫钩鏂鍔犮佸噺鍒1鏃=1+2+2鈥︹+99+100=1+100+2+99+3+97鈥︹=5050 妤间笂鐨勫お闅剧湅鎳備簡锛乷(鈺枴鈺)o
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 鍙傝冭祫鏂欙細骞虫柟宸叕寮 ...
绛旓細100鐨勫钩鏂-99鐨勫钩鏂=( 100+99 )脳(100 -99 )=199
绛旓細+鍘熷紡=(100^2-99^2)+(98^2-97^2)+...+(2^2-1)=(100+99)(100-99)+(98+97)(98-97)+...+(2+1)(2-1)=199+195+191+...+7+3 绛夊樊鏁板垪锛屽叡50涓暟锛屽叕宸负4 =锛199+3锛壝50/2锛5050
