`1/13 + 3/13.23 + 3/23.33 + .... + 3/1993.2003`
`=3/3.13 + 3/13.23 + 3/23.33 + .... + 3/1993.2003`
`=3/10(\frac{10}{3.13}+\frac{10}{13.23}+\frac{10}{23.33}+.....+\frac{10}{1993.2003})`
`=3/10(1/3 - 1/13 + 1/13 - 1/23 + 1/23 - 1/33 + ..... + 1/1993 - 1/2003)`
`=3/10(1/3 - 1/2003)`
`=3/10 . 2000/6009`
`=200/2003`