ESPA4122 Matematika Ekonomi - Deret

Introduction

This tutorial provides a comprehensive guide to understanding series in economic mathematics based on the content from the video "ESPA4122 Matematika Ekonomi - Deret." Series are fundamental in various economic calculations, making this topic essential for students and professionals in the field. In this guide, we will cover the definition of a series, types of series, and practical applications.

Step 1: Understanding Series

• A series is the sum of the terms of a sequence.
• It is crucial to know the difference between a sequence (ordered list of numbers) and a series (sum of those numbers).
• Example: The series of the first n natural numbers can be expressed as:
  • S = 1 + 2 + 3 + ... + n

Step 2: Types of Series

• Arithmetic Series

  • Defined by a constant difference between consecutive terms.
  • Formula to find the sum of the first n terms:
    • S_n = n/2 * (a + l)
      • Where:
        • n = number of terms
        • a = first term
        • l = last term

• Geometric Series

  • Each term is found by multiplying the previous term by a fixed, non-zero number.
  • Formula for the sum of the first n terms:
    • S_n = a * (1 - r^n) / (1 - r)
      • Where:
        • a = first term
        • r = common ratio
        • n = number of terms

Step 3: Practical Applications of Series

• Series are used in calculating present and future values in finance.
• They help in determining the total cost or revenue when dealing with fixed and variable costs over time.
• Example: Use an arithmetic series to calculate total salaries paid over a period when salaries increase annually.

Step 4: Common Pitfalls to Avoid

• Ensure you correctly identify whether a series is arithmetic or geometric before applying formulas.
• Double-check calculations, especially when summing large numbers of terms to avoid arithmetic errors.

Conclusion

Understanding series is essential for economic mathematics. This guide has introduced the basics of series, including definitions, types, formulas, and real-world applications. To further your knowledge, practice solving problems related to both arithmetic and geometric series, and explore their applications in financial scenarios.