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! + …………

**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

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