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![](https://rs.olm.vn/images/avt/0.png?1311)
a) \(A=\frac{15^{16}+1}{15^{17}+1}\)và\(B=\frac{15^{15}+1}{15^{16}+1}\)
ta có \(A=\frac{15^{16}}{15^{17}}\)và\(B=\frac{15^{15}}{15^{16}}\)
ta dễ nhận thấy phần cơ số của hai phân số A và B = nhau
mà phần mũ của các lũy thừa phân số A đều lớn hơn phân số B
\(\Rightarrow\frac{15^{16}}{15^{17}}>\frac{15^{15}}{15^{16}}\)
\(\Rightarrow\frac{15^{16}+1}{15^{17}+1}>\frac{15^{15}+1}{15^{16}+1}\)
\(\Rightarrow A>B\)
\(A=\frac{15^{16}+1}{15^{17}+1}vaB=\frac{15^{15}+1}{15^{16}+1}\)
+)Ta thấy\(A=\frac{15^{16}+1}{15^{17}+1}< 1\)
\(\Rightarrow A< \frac{15^{16}+1+14}{15^{17}+1+14}=\frac{15^{16}+15}{15^{17}+15}=\frac{15.\left(15^{15}+1\right)}{15.\left(15^{15}+1\right)}=\frac{15^{15}+1}{15^{16}+1}=B\)
Vậy A<B
b)Đề sai
Chúc bạn học tốt
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có:
\(A=\frac{10^{15}+1}{10^{16}+1}\)
\(10A=\frac{10^{16}+10}{10^{16}+1}\)
\(B=\frac{10^{16}+1}{10^{17}+1}\)
\(10B=\frac{10^{17}+10}{10^{17}+1}\)
Ta so sánh \(10A\) và \(10B\)
Có:
\(10A:\) Mẫu - tử = 9
\(10B:\) Mẫu - tử = 9
Lại có:
\(\frac{10^{16}+10}{10^{16}+1}\) \(-1\)\(=\frac{9}{10^{16}+1}\)
\(\frac{10^{17}+10}{10^{17}+1}-1=\frac{9}{10^{17}+1}\)
Vì \(\frac{9}{10^{16}+1}\)\(>\frac{9}{10^{17}+1}\)nên \(10A>10B\)
\(\Rightarrow\)\(A>B\)
Vậy \(A>B\)
Theo bải ra ta có:
A=\(\frac{10^{15}+1}{10^{16}+1}\)=> 10A =.\(\frac{10.\left(10^{15}+1\right)}{10^{16}+1}\)= \(\frac{10.10^{15}+1.10}{10^{16}+1}\)
= \(\frac{10.10^{15}+10}{10^{16}+1}\)=\(\frac{10^{16}+1+9}{10^{16}+1}\)= \(1+\frac{9}{10^{16}+1}\)
B= \(\frac{10^{16}+1}{10^{17}+1}\)=> 10B = \(\frac{10.\left(10^{16}+1\right)}{10^{17}+1}\)=\(\frac{10.10^{16}+1.10}{10^{17}+1}\)
= \(\frac{10.10^{16}+10}{10^{17}+1}\)= \(\frac{10^{17}+1+9}{10^{17}+1}\)= \(1+\frac{9}{10^{17}+1}\)
Vì 1=1 mà \(\frac{9}{10^{16}+1}\)> \(\frac{9}{10^{17}+1}\)nên => 10A > 10B => A>B
Vậy A>B.
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=\frac{10^{15}+1}{10^{16}+1}\)
\(\Rightarrow10A=\frac{10^{16}+10}{10^{16}+1}=\frac{\left(10^{16}+1\right)+9}{10^{16}+1}=1+\frac{9}{10^{16}+1}\)
\(A=\frac{10^{16}+1}{10^{17}+1}\)
\(\Rightarrow10B=\frac{10^{17}+10}{10^{17}+1}=\frac{\left(10^{17}+1\right)+9}{10^{17}+1}=1+\frac{9}{10^{17}+1}\)
Vì \(\frac{9}{10^{16}+1}>\frac{9}{10^{17}+1}\left(Do10^{16}+1< 10^{17}+1\right)\)
\(\Rightarrow10A>10B\)
\(\Rightarrow A>B\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có:
10A=1016+10/1016+1=1+(9/1016+1)
10B=1017+10/1017+1=1+(9/1017+1)
Vì 9/1016+1 > 9/1017+1 nên 10A>10B,do đó A>B
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có:\(\frac{2017^{18}+1}{2017^{17}+1}>1\)
\(\Rightarrow\frac{2017^{18}+1}{2017^{17}+1}>\frac{2017^{18}+1+2016}{2017^{17}+1+2016}=\frac{2017^{18}+2017}{2017^{17}+2017}\)\(=\frac{2017\left(2017^{17}+1\right)}{2017\left(2017^{16}+1\right)}=\frac{2017^{17}+1}{2017^{16}+1}\)
Vậy \(\frac{2017^{17}+1}{2017^{16}+1}< \frac{2017^{18}+1}{2017^{17}+1}\)
Thanks you nhiều nha,lần sau nhớ giải hộ mình các bài toán khác nữa nha
![](https://rs.olm.vn/images/avt/0.png?1311)
\(10A=\frac{10^{16}+10}{10^{16}+1}=\frac{10^{16}+1+9}{10^{16}+1}=1+\frac{9}{10^{16}+1}\)
\(10B=\frac{10^{17}+10}{10^{17}+1}=\frac{10^{17}+1+9}{10^{17}+1}=1+\frac{9}{10^{17}+1}\)
Nhận thấy: \(\frac{9}{10^{17}+1}< \frac{9}{10^{16}+1}\)=> 10B < 10A
=> A > B
A = ( 10^15+1 ) / ( 10^16+1 ) => 10A = ( 10^16+10 ) / ( 10^16+1 ) = 1 + ( 9/10^15+1 )
B = ( 10^16+1 ) / ( 10^17+1 ) => 10B = ( 10^17+10 ) / ( 10^17+1 ) = 1 + ( 9/10^16+1 )
Vì 10^15+1 < 10^16+1 nên 9/10^15+1 > 9/10^16+1 => 1 + ( 9/10^15+1 ) > 1 + ( 9/10^16+1 )
Vậy A > B
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