Question

So sánh:

\(M = \frac{13^{15}+1}{13^{16}+1}\) và \(N =\frac{13^{16}+1}{13^{17}+1}\)

Cứu tui nhe , tí nữa tui đi hok rồi:))

Answer 1

Ta có: \(M=\dfrac{13^{15}+1}{13^{16}+1}\)
        \(13M=\dfrac{3^{16}+1}{3^{16}+1}\)
        \(13M=1+\dfrac{12}{13^{16}+1}\)

         \(N=\dfrac{13^{16}+1}{13^{17}+1}\)
        \(13N=\dfrac{13^{17}+13}{13^{17}+1}\)
        \(13N=1+\dfrac{12}{13^{17}+1}\)
Vì \(\dfrac{12}{13^{16}+1}>\dfrac{12}{13^{17}+1}\) nên \(1+\dfrac{12}{13^{16}+1}>1+\dfrac{12}{13^{17}+1}\)
\(\rightarrow M>N\)
Vậy \(M>N\)