Create Going to zero or to infinity?.py

Author: Helmssyss

Solutions/Going to zero or to infinity?.py

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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.
+To avoid discussions about rounding, return the result truncated to 6 decimal places, for example:
+1.0000989217538616 will be truncated to 1.000098
+1.2125000000000001 will be truncated to 1.2125
+Remark
+Keep in mind that factorials grow rather rapidly, and you need to handle large inputs.
+Hint
+You could try to simplify the expression.
+"""
+
+import math
+
+def truncate(n, decimals=0):
+    multiplier = 10 ** decimals
+    return int(n * multiplier) / multiplier
+
+def going(n):
+    try:
+        count = -1
+        for i in range(0,n+1):
+            count += math.factorial(i)
+        return truncate((1/math.factorial(n))*count,6)
+    except OverflowError:
+        exit()