`A = 2/1 + 2/3 + 2/6 +.. + 2/5050`

`= 2( 2/2 + 2/6 + 2/12 + .. + 2/10100)` 

`=` `4( 1 + 1/6 + 1/12 + ... + 1/10100)`

`=` `4( 1 + 1/(2.3) + 1/(3.4) + ... + 1/(100.101) )`

`=` `4( 1 + 1/2 - 1/101 )`

`=` `4( 3/2 - 1/101 )`

`=` `4``( 303/202 - 2/202 )`

`=` `4. 301/202`

`=` `1204/202 `

`=` `602/101`