add kata

5kyu/going-to-zero-or-to-infinity/description.md

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+Consider the following numbers (where n! is factorial(n)):
+
+u1 = (1 / 1!) * (1!)
+u2 = (1 / 2!) * (1! + 2!)
+u3 = (1 / 3!) * (1! + 2! + 3!)
+...
+un = (1 / n!) * (1! + 2! + 3! + ... + n!)
+Which will win: 1 / n! or (1! + 2! + 3! + ... + n!)?
+
+Are these numbers going to 0 because of 1/n! or to infinity due to the sum of factorials or to another number?
+
+Task
+Calculate (1 / n!) * (1! + 2! + 3! + ... + n!) for a given n, where n is an integer greater or equal to 1.
+
+Your result should be within 10^-6 of the expected one.
+
+Remark
+Keep in mind that factorials grow rather rapidly, and you need to handle large inputs.
+
+Hint
+You could try to simplify the expression.

5kyu/going-to-zero-or-to-infinity/solution.ts

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+
+export function factorial(n: number): number {
+  let result = n;
+  for (let i = n - 1; i > 0; i--) {
+    result *= i;
+  }
+
+  return result;
+}
+
+// inclusive both sides
+export function partialFactorial(to: number, from: number): number {
+  if (to === from) return 1;
+
+  if (to > from) {
+    throw new Error('to must be less than from');
+  }
+
+  let result = from;
+  for (let i = from - 1; i >= to; i--) {
+    result *= i;
+  }
+
+  return result;
+}
+
+export function going(n: number): number {
+  // your code
+  let result = 1 / n;
+
+  for (let i = 2; i <= n; i++) {
+    result += 1 / partialFactorial(i, n);
+  }
+
+  return result;
+}

5kyu/going-to-zero-or-to-infinity/tests.ts

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+import {going} from './solution'
+import {assert} from "chai";
+
+function testing(n:number, expected:number) {
+  assert.approximately(going(n), expected, 1e-6)
+}
+
+describe("Fixed Tests going", function() {
+    it("Basic tests", function() {
+        testing(5, 1.275);
+        testing(6, 1.2125);
+        testing(7, 1.173214);
+    });
+});