Question

cho c = 4/3.5 + 4/5.7 + ...+4/97.99 và d = 18/2.5 + 18/5.8 + ... + 18/203.206. Tính c/d

 

Answer 1

`c = 4/(3 . 5) + 4/(5. 7) + ... + 4/(97. 99)`

`= 2 . (1/3 - 1/5 + 1/5 - 1/7 + ... + 1/97 - 1/99)`

`= 2 . (1/3 - 1/99)`

`= 2 . (33/99 - 1/99)`

`= 2 . 32/99`

`= 64/99`

`d = 18/(2 . 5) + 18/(5 . 8) +... + 18/(203 . 206)`

`= 6 . (1/2 - 1/5 + 1/5 - 1/8  +... + 1/203 - 1/206)`

`= 6 . (1/2 - 1/206)`

`= 6 . 102/206`

`=612/206`

`= 336/103`

`-> c/d = (64/99)/(336/103) = 412/2079`