Math Problem Statement

Write the following sums in sigma notation: \( \frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \dots + \frac{1}{1000} \).

Solution

The problem requires expressing the sum 13+14+15++11000\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 1n\frac{1}{n}, starting from n=3n = 3 and ending at n=1000n = 1000. Therefore, the sigma notation representation is:

n=310001n\sum_{n=3}^{1000} \frac{1}{n}

This compact form describes the summation of all terms in the sequence from n=3n = 3 to n=1000n = 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=1n = 1 instead of n=3n = 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.

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Math Problem Analysis

Mathematical Concepts

Sigma Notation
Series and Sequences

Formulas

Summation formula using \( \sum_{n=a}^b f(n) \)

Theorems

Properties of Arithmetic Series

Suitable Grade Level

Grades 10-12