Approximation of e

The Taylor series of the function $e^{x}$ is $e^{x} = \sum_{i \ge 0} \frac{x^{i}}{i!} \enspace .$

Note that this series has an infinite number of terms. However, for any $x$ we can get an approximation of $e^{x}$ by adding some of the first terms of the series (of course, the more terms, the better the result). In particular, chosing $x = 1$ gives us a method to compute $e \simeq 2'71828182845904523536$ : $e = \sum_{i \ge 0} \frac{1}{i!} \enspace .$

Write a program that, for every given natural number $n$ , prints the approximation of $e$ that we get by adding the $n$ first terms of the series above.

Input

Input consists of several natural numbers $n$ between 0 and 20.

Output

For every given $n$ , print with 10 digits after the decimal point the approximation of $e$ that we get by adding the $n$ first terms of the series above.

Observation

Because of overflow reasons, do all the computations for this exercise using real numbers.

Problem information

Author: Unknown
Translator: Carlos Molina

Generation: 2026-01-25T10:00:47.619Z