merge: Added Sum of GP (TheAlgorithms#807)

Author: SpiderMath

Maths/SumOfGeometricProgression.js

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+/*
+  Returns the sum of a geometric progression
+  Article on Geometric Progression: https://en.wikipedia.org/wiki/Geometric_series
+  Examples:
+  > sumOfGeometricProgression(2, 0.5, 6)
+  3.9375
+  > sumOfGeometricProgression(0.5, 10, 3)
+  55.5
+  > sumOfGeometricProgression(0.5, 10, Infinity)
+  Error: The geometric progression is diverging, and its sum cannot be calculated
+*/
+
+/**
+ *
+ * @param {Number} firstTerm The first term of the geometric progression
+ * @param {Number} commonRatio The common ratio of the geometric progression
+ * @param {Number} numOfTerms The number of terms in the progression
+ */
+function sumOfGeometricProgression (firstTerm, commonRatio, numOfTerms) {
+  if (!Number.isFinite(numOfTerms)) {
+    /*
+      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(commonRatio) < 1) return firstTerm / (1 - commonRatio)
+    throw new Error('The geometric progression is diverging, and its sum cannot be calculated')
+  }
+
+  if (commonRatio === 1) return firstTerm * numOfTerms
+
+  return (firstTerm * (Math.pow(commonRatio, numOfTerms) - 1)) / (commonRatio - 1)
+}
+
+export { sumOfGeometricProgression }

Maths/test/SumOfGeometricProgression.test.js

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+import { sumOfGeometricProgression } from '../SumOfGeometricProgression'
+
+describe('Sum Of Geometric Progression', () => {
+  it('should return the sum of a finite GP', () => {
+    expect(sumOfGeometricProgression(100, 1.5, 4)).toBe(812.5)
+  })
+
+  it('should return the sum of an infinite GP', () => {
+    expect(sumOfGeometricProgression(2, 0.5, Infinity)).toBe(4)
+  })
+})