feat: add Euler number approximation algorithm

Maths/EulerNumber.js

@@ -0,0 +1,25 @@
+/**
+ * @function eulerNumber
+ * @description Approximates Euler's number (e) using the formula:
+ *   e = sum(1/n!) for n from 0 to infinity.
+ *   This function computes e to a specified number of terms.
+ * @param {number} terms - Number of terms to use in approximation
+ * @returns {number} - Approximation of Euler's number e
+ * @see https://en.wikipedia.org/wiki/E_(mathematical_constant)
+ * @example eulerNumber(10) => 2.7182818011...
+ * @example eulerNumber(20) => 2.718281828459045
+ */
+const eulerNumber = (terms) => {
+  if (!Number.isInteger(terms) || terms < 1) {
+    throw new TypeError('Input must be a positive integer')
+  }
+  let result = 0
+  let factorial = 1
+  for (let i = 0; i < terms; i++) {
+    if (i > 0) factorial *= i
+    result += 1 / factorial
+  }
+  return result
+}
+
+export { eulerNumber }

Maths/test/EulerNumber.test.js

@@ -0,0 +1,46 @@
+import { eulerNumber } from '../EulerNumber.js'
+
+describe('eulerNumber', () => {
+  test('eulerNumber(1) returns 1', () => {
+    expect(eulerNumber(1)).toBe(1)
+  })
+
+  test('eulerNumber(2) returns 2', () => {
+    expect(eulerNumber(2)).toBe(2)
+  })
+
+  test('eulerNumber(5) approximates e', () => {
+    expect(eulerNumber(5)).toBeCloseTo(2.708, 2)
+  })
+
+  test('eulerNumber(10) approximates e closely', () => {
+    expect(eulerNumber(10)).toBeCloseTo(2.71828, 4)
+  })
+
+  test('eulerNumber(20) approximates e very closely', () => {
+    expect(eulerNumber(20)).toBeCloseTo(2.718281828459045, 10)
+  })
+
+  test('more terms give better approximation', () => {
+    const e = Math.E
+    expect(Math.abs(eulerNumber(20) - e)).toBeLessThan(
+      Math.abs(eulerNumber(5) - e)
+    )
+  })
+
+  test('throws TypeError for zero', () => {
+    expect(() => eulerNumber(0)).toThrow(TypeError)
+  })
+
+  test('throws TypeError for negative input', () => {
+    expect(() => eulerNumber(-10)).toThrow(TypeError)
+  })
+
+  test('throws TypeError for float input', () => {
+    expect(() => eulerNumber(10.5)).toThrow(TypeError)
+  })
+
+  test('throws TypeError for string input', () => {
+    expect(() => eulerNumber('10')).toThrow(TypeError)
+  })
+})