1. **State the problem:** We want to express the series $-1 + \frac{1}{2} - \frac{1}{3} + \frac{1}{4} - \cdots + \frac{1}{100}$ in sigma notation. 2. **Identify the pattern:** The series alternates signs starting with a negative term at $n=1$, and the denominators are consecutive integers from 1 to 100. 3. **General term:** The $n$th term can be written as $(-1)^n \cdot \frac{1}{n}$ because: - When $n=1$, $(-1)^1 = -1$, so the term is $-\frac{1}{1} = -1$. - When $n=2$, $(-1)^2 = 1$, so the term is $\frac{1}{2}$. - This matches the alternating signs. 4. **Sigma notation:** The series is $$\sum_{n=1}^{100} (-1)^n \frac{1}{n}$$ 5. **Explanation:** This notation means we sum the terms $(-1)^n \frac{1}{n}$ starting from $n=1$ up to $n=100$, which exactly reproduces the given series. **Final answer:** $$\sum_{n=1}^{100} (-1)^n \frac{1}{n}$$