Number Patterns

Consider the following number pattern: \[\frac{1}{2} = \frac{1}{1 \times 2} = 1 - \frac{1}{2}\] \[\frac{1}{6} = \frac{1}{2 \times 3} = \frac{1}{2} - \frac{1}{3}\] \[\frac{1}{12} = \frac{1}{3 \times 4} = \frac{1}{3} - \frac{1}{4}\] \[\frac{1}{20} = \frac{1}{4 \times 5} = \frac{1}{4} - \frac{1}{5}\] \[\dots\] \[\frac{1}{110} = \frac{1}{m \times k} = \frac{1}{m} - \frac{1}{k}\] \[\dots\]

1. Write down the \(5^{th}\) and the \(6^{th}\) row of the number pattern.
2. Find the integer values of \(m\) and \(k\).
3. Find a formula for the \(n^{th}\) row of the pattern in terms of \(n\).