1/2*-1+1/4*-1+1/6*-1+....1/100*-1

1/(2²-1)+1/(4²-1)+1/(6²-1)+....1/(100²-1)
=1/1*3+1/3*5+1/5*7+....1/99*101(裂项）
=1-1/3+1/3-1/5+1/5-1/7+....1/99-1/101（中间的消去）
=1-1/101
=100/101

2*-1是2的付一次方还是2乘以负一啊。

原式=1/（2+1）*（2+1）+1/（4-1）*（4+1）+····1/(100-1)*(100+1)
=1/1*3+1/2*4+····1/99*101
=1/2(2/1*3+2/3*5+····2/99*101)
=1/2(3-1/1*3+5-3/3*5+····101-99/99*101)
=1/2(1/1-1/3+1/3-1/5+····+1/99+1/101)
=1/2(1-1/101)
=50/101