1-2²+3²-4²+.............+99²-100²+101²

显示全部楼层 · 2012-7-17 13:56:37

原式=(1-2)(1+2)+(3-4)(3+4)+....+(99-100)(99+100)+101^2
=-(1+2)-(3+4)......-(99+100)+101^2
=-(1+2+3+4+...+99+100)+101^2
=-(1+100)*100/2+(100+1)^2
=-5050+100^2+200+1
=5151...

千问 · 2012-7-17 13:56:37

1^2-2^2=(1-2)*(1+2)=-1*(1+2)3^2-4^2=(3-4)*(3+4)=-1*(3+4)5^2-6^2=(5-6)*(5+6)=-1*(5+6)........99^2-100^2=-1*(99+100)原式 = -1(1+2+3+...+100)+101^2=-5050 + 10201=5151...

千问 · 2012-7-17 13:56:37

=(1+2)(1-2)+(3+4)(3-4)....+(99+100)(99-100)+101*101=-1*(1+2+3+4...+100)*100/2+10201=-1*5050+10201=5151...

千问 · 2012-7-17 13:56:37

3^2-2^2=(3+2)(3-2)=55^2-4^2=(5+4)(5-4)=97^2-6^2=(7+6)(7-6)=139^2-8^2=(9+8)(9-8)=17依此类推，得等差数列1+5+9+13+17+21+25+29·····+197+201=202X51/2=101X51=5151...

千问 · 2012-7-17 13:56:37

原式等于(1-2)*(1+2)+(3-4)*(3+4)...(99-100)*(99+100)+101^2=-(1+2+3+4+...+99+100)+101^2=101*51=5151...