1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8+1/8*9+1/9*10+.+1/96*97+1/97*98=

问题描述:

1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8+1/8*9+1/9*10+.+1/96*97+1/97*98=

1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8+1/8*9+1/9*10+.+1/96*97+1/97*98
=1-½+½-1/3+1/3-¼+¼-1/5+···+1/97-1/98
=1-1/98
=97/98