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

• Last Updated : 24 Mar, 2021

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! + …………

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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`

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