Question

So sánh M và N biết rằng: M=\(\frac{101^{102}+1}{101^{103}+1}\); N=\(\frac{101^{103}+1}{101^{104}+1}\)

Answer 1

Ta có : 

\(N=\frac{101^{103}+1}{101^{104}+1}< 1=\frac{101^{103}+1+100}{101^{104}+1+100}=\frac{101^{103}+101}{101^{104}+101}=\frac{101\left(101^{102}+1\right)}{101\left(101^{103}+1\right)}=\frac{101^{102}+1}{101^{103}+1}=M\)

Vậy\(N< M\)

Answer 2

Kết quả là:N<M

Answer 3

Ta có :

\(M=\frac{101^2+1}{101^3+1}\)

\(N=\frac{101^3+1}{101^4+1}< 1=\frac{101^3+1+100}{101^3+1+100}=\frac{101^3+101}{101^3+101}=\)\(\frac{101^2\cdot101+101\cdot1}{101^3\cdot101+101\cdot1}=\frac{101\cdot\left(101^2+1\right)}{101\cdot\left(101^3+1\right)}=\frac{101^2+1}{101^3+1}=M\)

\(\Rightarrow M>N\)

Answer 4

M<N nhé