绝对值数学题.....

因为1/10大于1/11,
1/11大于1/12,
......,
1/49大于1/50，
所以|1/10-1/11|=1/10-1/11,
|1/11-1/12|=1/11-1/12
......,
|1/49-1/50|=1/49-1/50,
所以原式=1/10-1/11-1/11+1/12-1/12+1/13-......+1/49-1/49+1/50
=1/10-2/11+1/50
=-17/275

因1/10>1/11,以下类同
故原式＝1/10-1/11-1/11+1/12-1/12+1/13-1/13+1/14+...+1/50
＝1/10-1/11-1/11＋1/50 （中间各项互相抵消）
＝1/10-2/11+1/50
＝(55-100+11)/50*11
＝-17/275

=1/10-1/11-1/11+1/12-1/12+1/13.....-1/48+1/49-1/49+1/50
=1/10-1/11-1/11+1/50
=-17/275