Question

a.(Cho a,b,n \(\in\) N* Hãy so sánh \(\frac{a+n}{b+n}\)và \(\frac{a}{b}\)

b.Cho \(A=\frac{10^{11}-1}{10^{12}-1}\) Và \(B=\frac{10^{10}+1}{10^{11}+1}\). So sánh A và B

Answer 1

a, Nếu\(\frac{a}{b}\)< 1 \(\Rightarrow\frac{a}{b}\)< \(\frac{a+n}{b+n}\)

Nếu \(\frac{a}{b}\)=1\(\Rightarrow\frac{a}{b}\)=\(\frac{a+n}{b+n}\)

Nếu \(\frac{a}{b}\)>1\(\frac{ }{ }\Rightarrow\frac{a}{b}\)>\(\frac{a+n}{b+n}\)

b,Ta có:

A\(=\frac{10^{11}-1}{10^{12}-1}\)<1   ( Vì tử < mẫu)

\(\Rightarrow\)A=\(\frac{10^{11}-1}{10^{12}-1}\)< \(\frac{10^{11}-1+11}{10^{12}-1+11}\)\(=\frac{10^{11}+10}{10^{12}+10}=\frac{10.\left(10^{10}+1\right)}{10.\left(10^{11}+1\right)}\)\(=\frac{10^{10}+1}{10^{11}+1}\)\(=\)B

Vậy A<B