# 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 + x^{2}/2! + x^{4}/4! + …………Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the

DSA Self Paced Courseat a student-friendly price and become industry ready. To complete your preparation from learning a language to DS Algo and many more, please referComplete Interview Preparation Course.In case you wish to attend

live classeswith experts, please referDSA Live Classes for Working ProfessionalsandCompetitive Programming Live for Students.

**Examples:**

Input:x = 1, N = 5Output:1.54308035714Input:x = 1, N = 10Output: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 <bits/stdc++.h>` `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

`<script>` `// Javascript program for the sum of` `// cosh(x) series` ` ` `// function to return the factorial of a number` ` ` `function` `fact( n) {` ` ` `let i = 1, fac = 1;` ` ` `for` `(i = 1; i <= n; i++)` ` ` `fac = fac * i;` ` ` `return` `fac;` ` ` `}` ` ` `// function to return the sum of the series` ` ` `function` `log_Expansion( x , n) {` ` ` `let sum = 0;` ` ` `let i = 0;` ` ` `for` `(i = 0; i < n; i++) {` ` ` `sum = sum + Math.pow(x, 2 * i) / fact(2*i);` ` ` `}` ` ` `return` `sum;` ` ` `}` ` ` `// Driver code` ` ` ` ` `let x = 1;` ` ` `let n = 10;` ` ` `document.write(log_Expansion(x, n).toFixed(11));` `// This code is contributed by shikhasingrajput` `</script>` |

**Output:**

1.54308063497