1²-2²+3²-4²+5²-6²…-100²+101²

1²-2²+3²-4²+5²-6²…-100²+101²
1²-2²+3²-4²+5²-6²…-100²+101²

1²-2²+3²-4²+5²-6²…-100²+101²
1²-2²+3²-4²+5²-6²+…+99²-100²
=(1-2)(1+2)+(3-4)(3+4)+.(99-100)(99+100)+101²
=-(1+2+3+4.+99+100)+101²
=-5050 +10201=5151

1²-2²+3²-4²+5²-6²+…+99²-100²+101²
=1²+3²-2²+5²-4²+…+101²-100²
=1+﹙3+2﹚﹙3-2﹚+﹙5+4﹚﹙5-4﹚+…（101+100﹚﹙101-100﹚
=1+2+3+4+…+100+101
=﹙1+101﹚×101÷2
=5151

=1+(3-2)(3+2)+(5-4)(5+4)+...(101-100)(101+100)
=1+2+3+...+101
=(101+1)*101/2=101*51=5151