Question

2分之1+6分之5+12分之11+20分之19+。。。。。+9702分之9701+9900分之9899要过程

Answer 1

2分之1+6分之5+12分之11+20分之19+。。。。。+9702分之9701+9900分之9899
=(1-1/2)+(1-1/6)+(1-1/12)+(1-1/20)+......+(1-1/9702)+(1-1/9900)
=-(1/2+1/6+1/12+1/20+.....+1/9702+1/9900)+99*1
=-[1/(1*2)+1/(2*3)++1/(3*4)+1/(4*5)+....+1/(98*99)+1/(99*100)]+99 .
=-1[(1/1-1/2)++(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+....+(1/98-1/99)+(1/99-1/100)]+99 .
=-1[(1/1+1/2+1/3+1/4+....+1/98+1/99)-(1/2+1/3+1/4+1/5+....+1/99+1/100)]+99
=-1(1-1/100)+99
=98+1/100=九十八又百分之一

Answer 2

1/2+5/6+11/12+19/20+...+9701/9702+9899/9900
=1-(1-1/2)+1-(1/2-1/3)+1-(1/3-1/4)+1-(1/4-1/5)+...+1-(1/98-1/99)+1-(1/99-1/100)
=99-(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/98-1/99+1/99-1/100)
=99-(1-1/100)
=9801/100