JavaScript: Sum of a geometric progression

JavaScript Math: Exercise-67 with Solution

Sum of Geometric Progression

Write a JavaScript program to calculate the sum of a geometric progression.

From Wikipedia,
In mathematics, a geometric series is the sum of an infinite number of terms that have a constant ratio between successive terms. For example, the series

is geometric, because each successive term can be obtained by multiplying the previous term by 1/2. In general, a geometric series is written as a + ar + ar² + ar³ + ..., where a is the coefficient of each term and r is the common ratio between adjacent terms. The geometric series had an important role in the early development of calculus, is used throughout mathematics, and can serve as an introduction to frequently used mathematical tools such as the Taylor series, the complex Fourier series, and the matrix exponential.

Sample Data:
(100, 2.5, 5) -> 6443.75
(0.5, 20, Infinity) -> Error

Sample Solution:

JavaScript Code:

/**
 * https://bit.ly/3gCyxWa 
 * first_Term: The first term of the geometric progression.
 * common_Ratio: The common ratio of the geometric progression.
 * num_Of_Terms: The number of terms in the progression.
 */
function sumOf_Geometric_Progression(first_Term, common_Ratio, num_Of_Terms) {
  // Check if the number of terms is finite
  if (!Number.isFinite(num_Of_Terms)) {
    /*
      If the number of Terms is Infinity, the common ratio needs to be less than 1 to be a convergent geometric progression
      Article on Convergent Series: https://en.wikipedia.org/wiki/Convergent_series
    */
    if (Math.abs(common_Ratio) < 1) return first_Term / (1 - common_Ratio);
    // Throw an error if the geometric progression is diverging
    throw new Error('The geometric progression is diverging, and its sum cannot be calculated');
  }
  // Calculate the sum of the geometric progression based on different scenarios
  if (common_Ratio === 1) return first_Term * num_Of_Terms;
  return (first_Term * (Math.pow(common_Ratio, num_Of_Terms) - 1)) / (common_Ratio - 1);
}

// Output the sum of geometric progressions for given parameters
console.log(sumOf_Geometric_Progression(100, 2.5, 5));
console.log(sumOf_Geometric_Progression(0.5, 20, Infinity));

Output:

6443.75
--------------------------------------------------------------------------------------
Uncaught Error: The geometric progression is diverging, and its sum cannot be calculated 
 at https://cdpn.io/cpe/boomboom/pen.js?key=pen.js-3a654673-3f71-908f-113a-2a3523b2059c:14

Flowchart:

Live Demo:

See the Pen javascript-math-exercise-67 by w3resource (@w3resource) on CodePen.

For more Practice: Solve these Related Problems:

• Write a JavaScript function that calculates the sum of a geometric progression given the first term, common ratio, and number of terms.
• Write a JavaScript function that computes the sum of an infinite geometric series when the common ratio's absolute value is less than one.
• Write a JavaScript function that validates the input parameters of a geometric progression before performing the sum calculation.
• Write a JavaScript function that returns the sum of a geometric series and formats the result to a fixed number of decimals.

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