Đáp án:
`\frac{2018^{99} -1 }{2018^{100} -1 }>\frac{2018^{98} -1 }{2018^{99} -1 }`
Giải thích các bước giải:
Đặt `A=\frac{2018^{99} -1 }{2018^{100} -1 }` và `B=\frac{2018^{98} -1 }{2018^{99} -1 }`
`A=\frac{2018^{99} -1 }{2018^{100} -1 }`
`=>2018A={2018(2018^{99} -1 )}/{2018^{100} -1 }`
`=>2018A={2018^{100} -2018}/{2018^{100} -1 }`
`=>2018A={(2018^{100}-1) -2017}/{2018^{100} -1 }`
`=>2018A=1-{2017}/{2018^{100} -1 }(1)`
`B=\frac{2018^{98} -1 }{2018^{99} -1 }`
`=>2018B={2018(2018^{98} -1 )}/{2018^{99} -1 }`
`=>2018B={2018^{99} -2018 }/{2018^{99} -1 }`
`=>2018B={2018^{99} -2018 }/{2018^{99} -1 }`
`=>2018B={(2018^{99} -1)-2017 }/{2018^{99} -1 }`
`=>2018B=1-{2017 }/{2018^{99} -1 }(2)`
Vì `2018^{99} -1 <2018^{100} -1`
`=>{2017}/{2018^{100} -1 }<{2017 }/{2018^{99} -1 }(3)`
Từ `(1),(2),(3)`
`=>2018A>2018B`
`=>A>B`
