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

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
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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 `

Output:

```1.54308063497
```

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