Question

48/49 47/48 51/52 50/51 smallest to largest

Answer 1

47/48 48/49 50/51 51/52

Answer 2

Notice that \[a_n=\frac n {n+1}\] is increasing sequence

Answer 3

Derivative of a_x with respect to x is \( \frac 1 {1+x^2}\) so it is always positive. So a_n is increasing.

Answer 4

\[\left\{\frac{48}{49},\frac{47}{48},\frac{51}{52},\frac{50}{51}\right\} \]Sorted low to high:\[\left\{\frac{47}{48},\frac{48}{49},\frac{50}{51},\frac{51}{52}\right\}\to \{0.979167,0.979592,0.980392,0.980769\} \]