1/8+1/24+1/48+1/100
=1/4×(1/2+1/6+1/12+1/25）
=1/4×(1/1*2+1/2*3+1/3*4+1/5*5)
=1/4×(1-1/2+1/2-1/3+1/3-1/4+1/25)
=1/4×(1-1/4+1/25)
=1/4×79/100
=79/400
怀疑你最后一个分数1/100应该是1/80
即：
1/8+1/24+1/48+1/80
=1/4×(1/2+1/6+1/12+1/20）
=1/4×(1/1*2+1/2*3+1/3*4+1/4*5)
=1/4×(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5)
=1/4×(1-1/5)
=1/4×4/5
=1/5