The problem requires expressing the sum $\frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \dots + \frac{1}{1000}$ in sigma notation.

Solution:

This is a series where each term is of the form $\frac{1}{n}$, starting from $n = 3$ and ending at $n = 1000$. Therefore, the sigma notation representation is:

$\sum_{n=3}^{1000} \frac{1}{n}$

This compact form describes the summation of all terms in the sequence from $n = 3$ to $n = 1000$.

Let me know if you'd like further details or have any questions!

Related Questions:

1. What does sigma notation represent in mathematics?
2. How do you determine the lower and upper bounds in sigma notation for a given series?
3. Can this series be evaluated to a numerical value? If so, how?
4. How does this summation relate to the harmonic series?
5. What happens if the series started at $n = 1$ instead of $n = 3$?

Tip:

When working with sigma notation, always identify the general term of the sequence and the range of the index to construct the correct summation.