`A= 1/5^1- 1/5^3 + 1/5^5 - 1/5^7+… + 1/5^99 - 1/5^101`
`= 1/5 - (1/5^3 - 1/5^5) - (1/5^7 - 1/5^9)-… - (1/5^97 - 1/5^99) - 1/5^101`
Ta có:
`1/5^3 > 1/5^5 => 1/5^3 - 1/5^5 > 0`
`1/5^7 > 1/5^9 => 1/5^7 - 1/5^9 > 0`
......................
`1/5^97 > 1/5^99 => 1/5^97 - 1/5^99 > 0`
mà `1/5^101 > 0`
`=> 1/5 - (1/5^3 - 1/5^5) - (1/5^7 - 1/5^9)-… - (1/5^97 - 1/5^99) - 1/5^101 < 1/5`
`=> A < 1/5` (đpcm)
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`B = 1/51+ 1/52+ 1/53+ 1/54+ ..... + 1/150 (100` số hạng)
`< 1/51+ 1/51+ 1/51+ 1/51+ ..... + 1/51 (100` số hạng)
`= 100/51 < 2`
mà `2 < 3`
`=> 1/51+ 1/52+ 1/53+ 1/54+ ..... + 1/150 < 3`
`=> B < 3` (đpcm)
(Chúc bạn học tốt)