1-2²+3²-4²+.+99²-100²+101²

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

1-2²+3²-4²+.+99²-100²+101²
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

5151
1-2²+3²-4²+.............+99²-100²+101²
=101+100+99+98+........+4+3+2+1
=101×(1+101)/2
=5151

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

=(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

1-2²+3²-4²+.............+99²-100²+101²
=1+(3+2)(3-2)+(5+4)(5-4)+...+(101+100)(101-100)
=1+5+9+13+...+201
=（1+201）*[（201-1）/2）+1]/2
=202*101/2
=10201.

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

=(1-2)*(1+2)+(3-4)*(3+4)+......+(99-100)*(99+100)+101*101= -1*（1+2+3+4+......+99+100）+101*101= - 101*50+101*101=101*51=5151

3^2-2^2=(3+2)(3-2)=5
5^2-4^2=(5+4)(5-4)=9
7^2-6^2=(7+6)(7-6)=13
9^2-8^2=(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