`5/( 3.6) + 5/( 6.9) + 5/( 9 . 12) + .... + 5/( 99 . 102)`
`= 5/3 . ( 3/( 3.6) + 3/( 6.9) + 3/( 9 . 12) + .... + 3/( 99 . 102))`
`= 5/3 . (1/3 - 1/6 + 1/6 - 1/9 + 1/9 - 1/12 + ... + 1/99 - 1/102)`
`= 5/3 . ( 1/3 - 1/102)`
`= 5/3 . 11/34`
`= 55/102`
``
`1/9 + 9/( 19 . 29) + 9/( 29 . 39) +.... + 9/( 1999 . 2009)`
`= 1/9 + (9/( 19 . 29) + 9/( 29 . 39) +.... + 9/( 1999 . 2009)`
` = 1/9+ [ 9/10 . (10/( 19 . 29) + 10/( 29 . 39) + .... + 10/( 1999 . 2009))`
`= 1/9 + [ 9/10 .( 1/19 - 1/29 + 1/29 - 1/39 + ... + 1/1999 - 1/2009)`
`=1/9 + [ 9/10 . ( 1/19 - 1/2009)]`
`= 1/9 + ( 9/10 . 1990/38171)`
`= 1/9 + 1791/38171`
`= 54290/343539`
