1.3 Represent the series \( \frac{2}{3}+\frac{3}{4}+\frac{4}{5}+\frac{5}{6}+\cdots+\frac{10}{11} \) using sigma notation.

To represent the series \( \frac{2}{3} + \frac{3}{4} + \frac{4}{5} + \frac{5}{6} + \cdots + \frac{10}{11} \) using sigma notation, follow these steps: 1. **Identify the Pattern:** - **Numerators:** Start at 2 and increase by 1 each term (2, 3, 4, ..., 10). - **Denominators:** Start at 3 and increase by 1 each term (3, 4, 5, ..., 11). 2. **Express the General Term:** Each term can be written as \( \frac{k}{k+1} \), where \( k \) starts at 2 and ends at 10. 3. **Write the Sigma Notation:** \[ \sum_{k=2}^{10} \frac{k}{k+1} \] **Final Answer:** \[ \sum_{k=2}^{10} \frac{k}{k+1} \]