`a)`
`3/1.4 + 3/4.7 + 3/7.10 + ... + 3/40.43`
`= 1- 1/4 + 1/4 - 1/7 + 1/7 - 1/10 + ... + 1/40 - 1/43`
`= 1 - 1/43`
`= 43/43- 1/43`
`= 42/43`
`b)`
`4/2.4 + 4/4.6 + 4/6.8 +... + 2/2016.2018`
`= 2 . ( 2/2.4 + 2/4.6 + 2/6.8 + ... + 2/2016.2018)`
`= 2 . ( 1/2 - 1/4 + 1/4 - 1/6 + 1/6 - 1/8 + ... + 1/2016 - 1/2018)`
`= 2 . (1/2 - 1/2018)`
`= 2 . (1009/2018 - 1/2018)`
`= 2 . 1004/1009`
`=2008/1009`
`c)`
`1/18 + 1/54 + 1/108 + ... + 1/990`
`=1/3.6 + 1/6.9 + 1/9.12 + ... +1/30.33`
`=1/3 . (1/3 - 1/6 +1/6 -1/9 +1/9 - 1/12 + ... + 1/30 -1/33)`
`=1/3 .(11/33 - 1/33)`
`=1/3 . 10/33`
`= 10/99`
