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Notice that \[a_n=\frac n {n+1}\] is increasing sequence
Derivative of a_x with respect to x is \( \frac 1 {1+x^2}\) so it is always positive. So a_n is increasing.
\[\left\{\frac{48}{49},\frac{47}{48},\frac{51}{52},\frac{50}{51}\right\} \]Sorted low to high:\[\left\{\frac{47}{48},\frac{48}{49},\frac{50}{51},\frac{51}{52}\right\}\to \{0.979167,0.979592,0.980392,0.980769\} \]
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