Let \(A = \large \frac{10^{1998} + 1}{10^{1999} + 1}\) and \(B = \large \frac{10^{1999} + 1}{10^{2000} + 1}\)

Which value is larger?

Guest Aug 10, 2020

#2**+1 **

**Let**

\(A = \dfrac{10^{1998} + 1}{10^{1999} + 1}\) and \(B=\dfrac{10^{1999} + 1}{10^{2000} + 1}\)

**Which value is larger?**

\(\begin{array}{|rcll|} \hline \mathbf{B} &=& \mathbf{ \dfrac{10^{1999} + 1}{10^{2000} + 1} } \\\\ B &=& \dfrac{10*10^{1998} + 1}{10*10^{1999} + 1} \\\\ B &=& \dfrac{10*\left(10^{1998} + \frac{1}{10} \right)}{10*\left(10^{1999} + \frac{1}{10}\right)} \\\\ \mathbf{B} &=& \mathbf{ \dfrac{10^{1998} + \frac{1}{10} }{10^{1999} + \frac{1}{10}} } \\ \hline \end{array}\)

\(\Rightarrow A \gt B\)

heureka Aug 12, 2020