Question

so sánh

\(\frac{100^{2015^{ }}+1}{100^{2005}+1}\) và\(\frac{100^{2016}+1}{100^{2006}+1}\)

Answer 1

\(\frac{100^{2015}+1}{100^{2015}+1}=1\)

\(\frac{100^{2016}+1}{100^{2016}+1}=1\)

Vì 1 = 1 nên \(\frac{100^{2015}+1}{100^{2015}+1}=\frac{100^{2016}+1}{100^{2016}+1}\)

Answer 2

à mình nhìn nhầm đề 

Mình giải nha

Đặt \(A=\frac{100^{2015}+1}{100^{2005}+1}\Rightarrow\frac{A}{100^{10}}=\frac{100^{2015}+1}{100^{2015}+100^{10}}=\frac{100^{2015}+100^{10}-999}{100^{2015}+100^{10}}=1-\frac{999}{100^{2015}+100^{10}}\)

Đặt \(B=\frac{100^{2016}+1}{100^{2006}+1}\Rightarrow\frac{B}{100^{10}}=\frac{100^{2016}+100^{10}-999}{100^{2016}+100^{10}}=1-\frac{999}{100^{2016}+100^{10}}\)

\(1-\frac{999}{100^{2015}+100^{10}}< 1-\frac{999}{100^{2016}+100^{10}}\Rightarrow A< B\)

Answer 3

Rõ ràng\(\frac{100^{2016}+1}{100^{2006}+1}\)<1 nên theo tính chất khi \(\frac{a}{b}\)< 1 => \(\frac{a}{b}\)<\(\frac{a+m}{b+m}\) => \(\frac{100^{2016}+1}{100^{2006}+1}\)<\(\frac{100^{2016}+1+99}{100^{2006}+1+99}\)

                                                                                                                                                            <\(\frac{100^{2016}+100}{100^{2006}+100}\)

=>\(\frac{100^{2016}+1}{100^{2006}+1}\)< \(\frac{100^{2016}+100}{100^{2006}+100}\) = \(\frac{100\left(100^{2015}+1\right)}{100\left(100^{2005}+1\right)}\)= \(\frac{\left(100^{2015}+1\right)}{\left(100^{2005}+1\right)}\)

Vậy\(\frac{100^{2016}+1}{100^{2006}+1}\) < \(\frac{\left(100^{2015}+1\right)}{\left(100^{2005}+1\right)}\)

Answer 4

Ninh Thế Quang Nhật sai rồi, \(^{100^{10\ne}999+1}\)