| 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 \(x\geq 1.\) |