# Program for sum of cosh(x) series upto Nth term

Last Updated : 25 May, 2022

Given two numbers x and N, the task is to find the value of cosh(x) from the series upto N terms.
The expansion of cosh(x) is given below:

cosh(x) = 1 + x2/2! + x4/4! + …………

Examples:

```Input: x = 1, N = 5
Output: 1.54308035714

Input: x = 1, N = 10
Output: 1.54308063497```

Approach:
The above series can be easily implemented using a factorial function and loops.
The nth term of the series is:

Below is the implementation of the above approach:

## C++

 `// C++ program for` `// the sum of cosh(x) series`   `#include ` `using` `namespace` `std;`   `// function to return the factorial of a number` `int` `fact(``int` `n)` `{`   `    ``int` `i = 1, fac = 1;` `    ``for` `(i = 1; i <= n; i++)` `        ``fac = fac * i;`   `    ``return` `fac;` `}`   `// function to return the sum of the series` `double` `log_Expansion(``double` `x, ``int` `n)` `{`   `    ``double` `sum = 0;` `    ``int` `i = 0;`   `    ``for` `(i = 0; i < n; i++) {`   `        ``sum = sum` `              ``+ ``pow``(x, 2 * i)` `                    ``/ fact(2 * i);` `    ``}`   `    ``return` `sum;` `}`   `// Driver code` `int` `main()` `{` `    ``double` `x = 1;` `    ``int` `n = 10;` `    ``cout << setprecision(12)` `         ``<< log_Expansion(x, n)` `         ``<< endl;`   `    ``return` `0;` `}`

## Java

 `// Java program for the sum of` `// cosh(x) series` `import` `java.util.*;`   `class` `GFG` `{`   `// function to return the factorial of a number` `static` `int` `fact(``int` `n)` `{` `    ``int` `i = ``1``, fac = ``1``;` `    ``for` `(i = ``1``; i <= n; i++)` `        ``fac = fac * i;`   `    ``return` `fac;` `}`   `// function to return the sum of the series` `static` `double` `log_Expansion(``double` `x, ``int` `n)` `{` `    ``double` `sum = ``0``;` `    ``int` `i = ``0``;`   `    ``for` `(i = ``0``; i < n; i++) ` `    ``{` `        ``sum = sum + Math.pow(x, ``2` `* i) / ` `                           ``fact(``2` `* i);` `    ``}`   `    ``return` `sum;` `}`   `// Driver code` `public` `static` `void` `main(String[] args) ` `{` `    ``double` `x = ``1``;` `    ``int` `n = ``10``;` `    ``System.out.println(log_Expansion(x, n));` `}` `}`   `// This code is contributed by 29AjayKumar`

## Python3

 `# Python3 program for the Sum of cosh(x) series`   `# function to return the factorial of a number` `def` `fact(n):`   `    ``i, fac ``=` `1``, ``1` `    ``for` `i ``in` `range``(``1``, n ``+` `1``):` `        ``fac ``=` `fac ``*` `i`   `    ``return` `fac`   `# function to return the Sum of the series` `def` `log_Expansion(x, n):`   `    ``Sum` `=` `0` `    ``i ``=` `0`   `    ``for` `i ``in` `range``(n):`   `        ``Sum` `=` `Sum` `+` `pow``(x, ``2` `*` `i) ``/` `fact(``2` `*` `i)`   `    ``return` `Sum`   `# Driver code` `x ``=` `1` `n ``=` `10` `print``(log_Expansion(x, n))`   `# This code is contributed by Mohit Kumar`

## C#

 `// C# program for the sum of` `// cosh(x) series` `using` `System;`   `class` `GFG` `{`   `// function to return the ` `// factorial of a number` `static` `int` `fact(``int` `n)` `{` `    ``int` `i = 1, fac = 1;` `    ``for` `(i = 1; i <= n; i++)` `        ``fac = fac * i;`   `    ``return` `fac;` `}`   `// function to return the sum of the series` `static` `double` `log_Expansion(``double` `x, ``int` `n)` `{` `    ``double` `sum = 0;` `    ``int` `i = 0;`   `    ``for` `(i = 0; i < n; i++) ` `    ``{` `        ``sum = sum + Math.Pow(x, 2 * i) / ` `                        ``fact(2 * i);` `    ``}`   `    ``return` `sum;` `}`   `// Driver code` `public` `static` `void` `Main(String[] args) ` `{` `    ``double` `x = 1;` `    ``int` `n = 10;` `    ``Console.WriteLine(log_Expansion(x, n));` `}` `}`   `// This code is contributed by PrinciRaj1992`

## Javascript

 ``

Output:

`1.54308063497`

Time Complexity: O(n2), where n represents the value of the given integer.
Auxiliary Space: O(1), no extra space is required, so it is a constant.

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