Question

So sánh lũy thừa sau:

a)(\(\frac{1}{31}\))\(^7\)và (\(\frac{1}{17}\))\(^9\)
b)A=\(\frac{10^{15}+1}{10^{16}+1}\) và B=\(\frac{10^{16}+1}{10^{17}+1}\)

Mk đang cần gấp,ai nhanh mk sẽ tick nha =))))
 

Answer 1

b) Áp dụng  tính chất

\(\frac{a}{b}< 1\Rightarrow\frac{a}{b}< \frac{a+m}{b+m}\left(m\in N\right)\)

Ta có: \(B=\frac{10^{16}+1}{10^{17}+1}< \frac{10^{16}+1+9}{10^{17}+1+9}=\frac{10^{16}+10}{10^{17}+10}=\frac{10.\left(10^{15}+1\right)}{10.\left(10^{16}+1\right)}=\frac{10^{15}+1}{10^{16}+1}=A\)

\(\Rightarrow B< A\)

Answer 2

\(B< 1\Rightarrow\frac{10^{16}+1}{10^{17}+1}< \frac{10^{16}+1+9}{10^{17}+1+9}=\frac{10^{16}+10}{10^{17}+10}=\frac{10\left(10^{15}+1\right)}{10\left(10^{16}+1\right)}=\frac{10^{15}+1}{10^{16}+1}=A\)

\(\Rightarrow A>B\)