Power Series Calculator

Step-by-Step Guide to Using the Power Series Calculator

Introduction

This Power Series Calculator is designed to compute the sum of a specified series to a given number of terms, evaluate the exact value of the series, and present both absolute and relative errors. Follow these steps to utilize the calculator effectively.

Step 1: Enter the x Value

• Locate the “x Value” Field: Look for the input field labeled “x Value”.
• Input a Number: Enter a number within the range of -100 to 100 into this field. You can use decimal numbers with two decimal places (e.g., -99.99, 0, 50.78).
• Mandatory Field: Inputting a value here is required. Ensure it meets the validation constraints.

Step 2: Specify the Number of Terms

• Locate the “Number of Terms” Field: This field is labeled accordingly.
• Enter a Whole Number: Input a whole number between 1 and 50. This corresponds to how many terms of the series you want to calculate.
• Validation: The field is compulsory, so be sure to provide a valid input.

Step 3: Choose the Series Type

• Access the “Series Type” Dropdown: This selection field provides multiple series options.
• Select an Option: Choose from the following series types:
  • Exponential Series (e^x)
  • Sine Series (sin x)
  • Cosine Series (cos x)
  • Geometric Series (1/(1-x))
• Mandatory Selection: You must pick one of the available series types to proceed.

Step 4: Review the Results

Once all inputs are provided, the calculator will display the results:

• Series Sum: The computed sum of the series for the number of terms specified, rounded to six decimal places.
• Exact Value: The exact analytical value of the entire series, rounded to six decimal places.
• Absolute Error: The difference between the series sum and the exact value, shown with six decimal places of precision.
• Relative Error (%): The error relative to the exact value, expressed as a percentage and displayed with four decimal places.