1+1/(1*3)+1/(2*3)+1/(2*5)+1/(3*5)+1/(3*7)+1/(4*7)+1/(4*9)怎么计算

1+1/(1*3)+1/(2*3)+1/(2*5)+1/(3*5)+1/(3*7)+1/(4*7)+1/(4*9)
= 1 + 1/3 + (1/2 - 1/3) + (1/3)(1/2 - 1/5) + (1/2)(1/3 - 1/5) + (1/4)(1/3 - 1/7) + (1/3)(1/4 - 1/7) + (1/5)(1/4 - 1/9)
= 1 + (1/3)(1 - 1 + 1/2 + 1/2 + 1/4 + 1/4) + 1/2 + (1/5)(-1/3 - 1/2 + 1/4 - 1/9) + (1/7)(-1/4 - 1/3 )
= 1 + (1/3)(3/2) + 1/2 + (1/5)(-25/36) + (1/7)(7/12)
= 2 - 5/36 - 1/12
= 16/9
= 1 and 7/9

这是带分数，中文读作 “一 又 九分之七”；
英文中称为 mixed number, 读作 “one and 7 over nine”

16/9 是假分数(Improper fraction),
汉语读作 “九分之十六”；
英文读作 “sixteen over nine”