$5$) `2/{9.11} + 2/{11.13} + 2/{13.15} + .... + 2/{221.223}`
`= 1/9 - 1/11 + 1/11 - 1/13 + 1/13 - 1/15 + .... + 1/221 - 1/223`
`= 1/9 - 1/223`
`= {214}/{2007}`
$6$) `5/{11.16} + 5/{16.21} + ..... + 5/{191.196}`
`= 1/11 - 1/16 + 1/16 - 1/21 + .... + 1/191 - 1/196`
`= 1/11 - 1/196`
`= 185/2156`
$7$) `1/{10.13} + 1/{13.16} + .... + 1/{331.334}`
`= 1/3 . (3/{10.13} + 3/{13.16} + .... + 3/{331.334})`
`= 1/3 . (1/10 - 1/13 + 1/13 - 1/16 + .... + 1/331 - 1/334)`
`= 1/3 . (1/10 - 1/334)`
`= {27}/{835}`
$8$) `5/{1.3} + 5/{3.5} + 5/{5.7} + ..... + 5/{1001.1003}`
`= 5/2 . (2/{1.3} + 2/{3.5} +2/{5.7} + ..... + 2/{1001.1003})`
`= 5/2 . {1002}/{1003}`
`= {2505}/{1003}`
