简便计算1/2候议的采案*2/3+1/3*2/4+1/4*2/5+…+1/99*2/100

1/2*2/3+1/3指*2/4+1/4*2/5+…+1/99*2/100
=2*(1/2*1/3+1/3*1/4+1/4*1/5+…+唱蒸移1/99*1/100)
=2*(1/2-1/3+1/3-1/4+1/4-1/5+…+1/99-1/100)
=2*(1/2-1/100)
=2*49/100
=49/50