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

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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:**
$$
\sum_{k=2}^{10} \frac{k}{k+1}
$$
$$ \sum_{k=2}^{10} \frac{k}{k+1} $$

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

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