# Sum of the Tan(x) expansion upto N terms

Given two integers N and X. The task is to find the sum of tan(x) series up to N terms.

The series :

x + x3/3 + 2x5/15 + 17x7/315 + 62x9/2835……..

Examples:

Input : N = 6, X = 1
Output :The value from the expansion is 1.55137626113259

Input : N = 4, X = 2
Output :The value from the expansion is 1.52063492063426

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

Approach :
The expansion of tan(x) is shown here. Compute the each term using a simple loops and get the required answer.

## C++

 `// CPP program to find tan(x) expansion ` `#include ` `using` `namespace` `std; ` ` `  `// Function to find factorial of a number ` `int` `fac(``int` `num) ` `{ ` `    ``if` `(num == 0) ` `        ``return` `1; ` ` `  `    ``// To store factorial of a number ` `    ``int` `fact = 1; ` `    ``for` `(``int` `i = 1; i <= num; i++) ` `        ``fact = fact * i; ` ` `  `    ``// Return the factorial of a number ` `    ``return` `fact; ` `} ` ` `  `// Function to find tan(x) upto n terms ` `void` `Tanx_expansion(``int` `terms, ``int` `x) ` `{ ` `    ``// To store value of the expansion ` `    ``double` `sum = 0; ` ` `  `    ``for` `(``int` `i = 1; i <= terms; i += 1) { ` `        ``// This loops here calculate Bernoulli number ` `        ``// which is further used to get the coefficient ` `        ``// in the expansion of tan x ` `        ``double` `B = 0; ` `        ``int` `Bn = 2 * i; ` `        ``for` `(``int` `k = 0; k <= Bn; k++) { ` `            ``double` `temp = 0; ` `            ``for` `(``int` `r = 0; r <= k; r++) ` `                ``temp = temp + ``pow``(-1, r) * fac(k) * ``pow``(r, Bn)  ` `                                     ``/ (fac(r) * fac(k - r)); ` ` `  `            ``B = B + temp / ((``double``)(k + 1)); ` `        ``} ` `        ``sum = sum + ``pow``(-4, i) * (1 - ``pow``(4, i)) * B *  ` `                               ``pow``(x, 2 * i - 1) / fac(2 * i); ` `    ``} ` ` `  `    ``// Print the value of expansion ` `    ``cout << setprecision(10) << sum; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `n = 6, x = 1; ` ` `  `    ``// Function call ` `    ``Tanx_expansion(n, x); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java program to find tan(x) expansion ` `class` `GFG ` `{ ` ` `  `// Function to find factorial of a number ` `static` `int` `fac(``int` `num) ` `{ ` `    ``if` `(num == ``0``) ` `        ``return` `1``; ` ` `  `    ``// To store factorial of a number ` `    ``int` `fact = ``1``; ` `    ``for` `(``int` `i = ``1``; i <= num; i++) ` `        ``fact = fact * i; ` ` `  `    ``// Return the factorial of a number ` `    ``return` `fact; ` `} ` ` `  `// Function to find tan(x) upto n terms ` `static` `void` `Tanx_expansion(``int` `terms, ``int` `x) ` `{ ` `    ``// To store value of the expansion ` `    ``double` `sum = ``0``; ` ` `  `    ``for` `(``int` `i = ``1``; i <= terms; i += ``1``) ` `    ``{ ` `         `  `        ``// This loops here calculate Bernoulli number ` `        ``// which is further used to get the coefficient ` `        ``// in the expansion of tan x ` `        ``double` `B = ``0``; ` `        ``int` `Bn = ``2` `* i; ` `        ``for` `(``int` `k = ``0``; k <= Bn; k++)  ` `        ``{ ` `            ``double` `temp = ``0``; ` `            ``for` `(``int` `r = ``0``; r <= k; r++) ` `                ``temp = temp + Math.pow(-``1``, r) * fac(k) *  ` `                              ``Math.pow(r, Bn) / (fac(r) *  ` `                                                 ``fac(k - r)); ` ` `  `            ``B = B + temp / ((``double``)(k + ``1``)); ` `        ``} ` `        ``sum = sum + Math.pow(-``4``, i) *  ` `               ``(``1` `- Math.pow(``4``, i)) * B *  ` `                    ``Math.pow(x, ``2` `* i - ``1``) / fac(``2` `* i); ` `    ``} ` ` `  `    ``// Print the value of expansion ` `    ``System.out.printf(``"%.9f"``, sum); ` `} ` ` `  `// Driver code ` `public` `static` `void` `main(String[] args)  ` `{ ` `    ``int` `n = ``6``, x = ``1``; ` ` `  `    ``// Function call ` `    ``Tanx_expansion(n, x); ` `} ` `} ` ` `  `// This code is contributed by Rajput-Ji `

## C#

 `// C# program to find tan(x) expansion ` `using` `System; ` `     `  `class` `GFG ` `{ ` ` `  `// Function to find factorial of a number ` `static` `int` `fac(``int` `num) ` `{ ` `    ``if` `(num == 0) ` `        ``return` `1; ` ` `  `    ``// To store factorial of a number ` `    ``int` `fact = 1; ` `    ``for` `(``int` `i = 1; i <= num; i++) ` `        ``fact = fact * i; ` ` `  `    ``// Return the factorial of a number ` `    ``return` `fact; ` `} ` ` `  `// Function to find tan(x) upto n terms ` `static` `void` `Tanx_expansion(``int` `terms, ``int` `x) ` `{ ` `    ``// To store value of the expansion ` `    ``double` `sum = 0; ` ` `  `    ``for` `(``int` `i = 1; i <= terms; i += 1) ` `    ``{ ` `         `  `        ``// This loop here calculates  ` `        ``// Bernoulli number which is  ` `        ``// further used to get the coefficient ` `        ``// in the expansion of tan x ` `        ``double` `B = 0; ` `        ``int` `Bn = 2 * i; ` `        ``for` `(``int` `k = 0; k <= Bn; k++)  ` `        ``{ ` `            ``double` `temp = 0; ` `            ``for` `(``int` `r = 0; r <= k; r++) ` `                ``temp = temp + Math.Pow(-1, r) * fac(k) *  ` `                              ``Math.Pow(r, Bn) / (fac(r) *  ` `                                                 ``fac(k - r)); ` ` `  `            ``B = B + temp / ((``double``)(k + 1)); ` `        ``} ` `        ``sum = sum + Math.Pow(-4, i) *  ` `               ``(1 - Math.Pow(4, i)) * B *  ` `                    ``Math.Pow(x, 2 * i - 1) / fac(2 * i); ` `    ``} ` ` `  `    ``// Print the value of expansion ` `    ``Console.Write(``"{0:F9}"``, sum); ` `} ` ` `  `// Driver code ` `public` `static` `void` `Main(String[] args)  ` `{ ` `    ``int` `n = 6, x = 1; ` ` `  `    ``// Function call ` `    ``Tanx_expansion(n, x); ` `} ` `} ` ` `  `// This code is contributed by 29AjayKumar `

Output:

```1.551373344
```

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Improved By : Rajput-Ji, 29AjayKumar

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