Question

So sánh 

M=\(\dfrac{17^{20}+1}{17^{19}+1}\) và N=\(\dfrac{17^{17}+1}{17^{16}+1}\)

Answer 1

\(\frac{M}{17}=\frac{17^{20}+1}{17^{20}+17}=\frac{17^{20}+17-16}{17^{20}+17}=1-\frac{16}{17^{20}+17}\)

\(\frac{N}{17}=\frac{17^{17}+1}{17^{17}+17}=\frac{17^{17}+17-16}{17^{17}+17}=1-\frac{16}{17^{17}+17}\)

Ta có: \(17^{20}+17>17^{17}+17\)

=>\(\frac{16}{17^{20}+17}<\frac{16}{17^{17}+17}\)

=>\(-\frac{16}{17^{20}+17}>-\frac{16}{17^{17}+17}\)

=>\(-\frac{16}{17^{20}+17}+1>-\frac{16}{17^{17}+17}+1\)

=>\(\frac{M}{17}>\frac{N}{17}\)

=>M>N