Question

So sánh: A = 10²⁰¹⁵ +1 phần 10²⁰¹⁶ +1 và B = 10²⁰¹⁶ +1 phần 10²⁰¹⁷ +1

Answer 1

\(A=\frac{10^{2015}+1}{10^{2016}+1}\Rightarrow10A=\frac{10.\left(10^{2015}+1\right)}{10^{2016}+1}=\frac{10^{2016}+10}{10^{2016}+1}\)

\(A=\frac{10^{2016}+1+9}{10^{2016}+1}=\frac{10^{2016}+1}{10^{2016}+1}+\frac{9}{10^{2016}+1}=1+\frac{9}{10^{2016}+1}\)

\(B=\frac{10^{2016}+1}{10^{2017}+1}\Rightarrow10B=\frac{10.\left(10^{2016}+1\right)}{10^{2017}+1}=\frac{10^{2017}+10}{10^{2017}+1}\)

\(B=\frac{10^{2017}+1+9}{10^{2017}+1}=\frac{10^{2017}+1}{10^{2017}+1}+\frac{9}{10^{2017}+1}=1+\frac{9}{10^{2017}+1}\)

Vì 10²⁰¹⁶+1 < 10²⁰¹⁷+1

=>\(\frac{9}{10^{2016}+1}>\frac{9}{10^{2017}+1}\)

=>\(1+\frac{9}{10^{2016}+1}>1+\frac{9}{10^{2017}+1}\)

=>10A > 10B

=>A > B

Answer 2

\(B=\frac{10^{2016}+1}{10^{2017}+1}<\frac{10^{2016}+1+9}{10^{2017}+1+9}\)

      \(=\frac{10^{2016}+10}{10^{2017}+10}\)

      \(=\frac{10.\left(10^{2015}+1\right)}{10.\left(10^{2016}+1\right)}\)

      \(=\frac{10^{2015}+1}{10^{2016}+1}=A\)

\(\Rightarrow\) B<A

Answer 3

\(10A=\frac{10\left(10^{2015}+1\right)}{10^{2016}+1}=\frac{10^{2016}+10}{10^{2016}+1}=\frac{10^{2016}+1+9}{10^{2016}+1}=\frac{10^{2016}+1}{10^{2016}+1}+\frac{9}{10^{2016}+1}=1+\frac{9}{10^{2016}+1}\)

\(10B=\frac{10\left(10^{2016}+1\right)}{10^{2017}+1}=\frac{10^{2017}+10}{10^{2017}+1}=\frac{10^{2017}+1+9}{10^{2017}+1}=\frac{10^{2017}+1}{10^{2017}+1}+\frac{9}{10^{2017}+1}=1+\frac{9}{10^{2017}+1}\)

vì 10²⁰¹⁶+1<10²⁰¹⁷+1

=>\(\frac{9}{10^{2016}+1}>\frac{9}{10^{2017}+1}\)

=>A>B

Answer 4

m.n ns cụ thể đi