要简算 1/1*2*3+1/2*3*4+1/3*4*5+...+1/98*99*100+1/99*100*101

要简算 1/1*2*3+1/2*3*4+1/3*4*5+...+1/98*99*100+1/99*100*101
要简算
1/1*2*3+1/2*3*4+1/3*4*5+...+1/98*99*100+1/99*100*101

要简算 1/1*2*3+1/2*3*4+1/3*4*5+...+1/98*99*100+1/99*100*101
(4/1*2*3*4+1/1*2*3*4)+(6/3*4*5*6+3/3*4*5*6)+……+(100/97*98*99*100+97/97*98*99*100)+1/99*100*101
=1/2(1/1*2-1/3*4)+1/2(1/3*4-1/5*6)+……+1/2（1/97*98-1/99*100）+1/99*100*101
=1/2（1/1*2-1/3*4+1/3*4-1/5*6+……+1/97*98-1/99*100）+1/99*100*101
=1/2（1/1*2-1/99*100）+1/99*100*101
=1/4-1/99*100*2+1/99*100*101
=1/4-101/99*100*2*101+2/99*100*2*101
=1/4-99/99*100*2*101
=1/4-1/100*101*2
=50*101/200*101-1/200*101
=50*101-1/200*101
=5049/20200