`a, 1/3 + 2/3 + ....... + 3 1/3 + 3 2/3`
`= (1/3 + 3 2/3) xx [(3 2/3 - 1/3) : 1/3 + 1) : 2]`
`= 3 3/3 xx [(3 1/3 : 1/3 + 1) : 2]`
`= 4 xx [(10/3 : 1/3 + 1) : 2]`
`= 4 xx [(10 + 1) : 2]`
`= 4 xx (11 : 2)`
`= 4 xx 5,5`
`= 22`
`b, 9 + 9/2 + 9/4 + 9/8 + ......... + 9/128 + 9/256`
`= 9 + 9/2 + 9/2 - 9/4 + 9/4 - 9/8 + ... + 9/64 - 9/128 + 9/128 - 256`
`= 9 + 9/2 + 9/2 - 9/256`
`= (2304 + 1152 + 1152 + 9)/256`
`= 4617/256`
P/s : Ở câu b, chúng ta thấy rằng :
`9/4 = 9/2 - 9/4`
`9/8 = 9/4 - 9/8`
`........................`
`c, 5/3 + 5/ (3 xx 5) + 5/(5xx 7) + ... + 5/ (101 xx 103)`
`= 5/2 xx [2/5 xx (5/3 + 5/ (3 xx 5) + 5/(5xx 7) + ... + 5/ (101 xx 103))]`
`= 5/2 xx (2/3 + 2/(3 xx 5) + 2/(5 xx 7) + ... + 2/(101xx103)`
`= 5/2 xx (2/3 + 2/3 - 2/5 + 2/5 - 2/7 + ... + 2/101 - 2/103`
`= 5/2 xx (2/3 + 2/3 - 2/103)`
`= 5/2 xx (206 + 206 - 6)/309`
`= 5/2 xx 406/309`
`= 1015/309`
