Question

So sánh A và B, biết

A=\(\frac{10^{15}+1}{10^{16}+1}\)

B=\(\frac{10^{16}+1}{10^{17}+1}\)

Mong các bạn viết đầy đủ cách làm!!

Answer 1

Ta có:

\(A=\frac{10^{15}+1}{10^{16}+1}=\frac{10^{16}+10}{10^{16}+1}=\frac{10^{16}+1+9}{10^{16}+1}=1+\frac{9}{10^{16}+1}\)

\(B=\frac{10^{16}+1}{10^{17}+1}=\frac{10^{17}+10}{10^{17}+1}=\frac{10^{17}+1+9}{10^{17}+1}=1+\frac{9}{10^{17}+1}\)

Vì \(\frac{1}{10^{16}+1}>\frac{1}{10^{17}+1}\)

\(\Rightarrow\frac{9}{10^{16}+1}>\frac{9}{10^{17}+1}\)

\(\Rightarrow1+\frac{9}{10^{16}+1}>1+\frac{9}{10^{17}+1}\)

\(\Rightarrow A>B\)

Answer 2

bạn tham khảo nha: hoc24.vn/hoi-dap/question/31717.html