Related Articles
Sum of the Tan(x) expansion upto N terms
• Difficulty Level : Basic
• Last Updated : 14 Apr, 2021

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

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`

## Python3

 `# Python3 program to find tan(x) expansion` `# Function to find factorial of a number``def` `fac(num):``    ``if` `(num ``=``=` `0``):``        ``return` `1``;` `    ``# To store factorial of a number``    ``fact ``=` `1``;``    ``for` `i ``in` `range``(``1``, num ``+` `1``):``        ``fact ``=` `fact ``*` `i;` `    ``# Return the factorial of a number``    ``return` `fact;` `# Function to find tan(x) upto n terms``def` `Tanx_expansion(terms, x):` `    ``# To store value of the expansion``    ``sum` `=` `0``;` `    ``for` `i ``in` `range``(``1``, terms ``+` `1``):` `        ``# This loops here calculate Bernoulli number``        ``# which is further used to get the coefficient``        ``# in the expansion of tan x``        ``B ``=` `0``;``        ``Bn ``=` `2` `*` `i;``        ``for` `k ``in` `range``(Bn ``+` `1``):``            ``temp ``=` `0``;``            ``for` `r ``in` `range``(``0``, k ``+` `1``):``                ``temp ``=` `temp ``+` `pow``(``-``1``, r) ``*` `fac(k) \``                    ``*` `pow``(r, Bn) ``/` `(fac(r) ``*` `fac(k ``-` `r));` `            ``B ``=` `B ``+` `temp ``/` `((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``    ``print``(``"%.9f"` `%``(``sum``));` `# Driver code``if` `__name__ ``=``=` `'__main__'``:``    ``n, x ``=` `6``, ``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`

## Javascript

 ``
Output:
`1.551373344`

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.  To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

In case you wish to attend live classes with industry experts, please refer DSA Live Classes

My Personal Notes arrow_drop_up