Table

Table 2: TABLE 2

	To Show ${\{ s}_{n}\}$ Is Decreasing	To Show $\{ s_{n}\}$ Is Increasing
Algebraic Difference	Show $s_{n+1}-s_{n}<0$ for all $n\geq 1.$	Show $s_{n+1}-s_{n}>0$ for all $n\geq 1.$
Algebraic Ratio	If $s_{n}>0$ for all $n\geq 1,$ show $\dfrac{s_{n+1}}{s_{n}} <1$ for all $n\geq 1.$	If $s_{n}>0$ for all $n\geq 1,$ show $\dfrac{s_{n+1}}{s_{n}}>1$ for all $n\geq 1.$
Derivative	Show the derivative of a related function $f$ of $\{s_{n}\}$ is negative for all $x\geq 1.$	Show the derivative of a related function $f$ of $\{s_{n}\}$ is positive for all $x\geq 1.$