# Sum of N terms in the expansion of Arcsin(x)

Given two integers N and X, the task is to find the value of Arcsin(x) using expansion upto N terms.

Examples:

Input: N = 4, X = 0.5
Output: 0.5233863467
Sum of first 4 terms in the expansion of Arcsin(x) for
x = 0.5 is 0.5233863467.

Input: N = 8, X = -0.5
Output: -0.5233948501

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

Approach: The expansion of arcsin(x) is given by : Note: |x| < 1

The above expansion is solved by using two variables maintaining the numerator and the denominator.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach ` `#include ` `using` `namespace` `std; ` ` `  `// Function to find the arcsin(x) ` `void` `find_Solution(``double` `x, ``int` `n) ` `{ ` `    ``double` `sum = x, e = 2, o = 1, p = 1; ` `    ``for` `(``int` `i = 2; i <= n; i++) { ` ` `  `        ``// The power to which 'x' is raised ` `        ``p += 2; ` ` `  `        ``sum += (``double``)(o / e) * (``double``)(``pow``(x, p) / p); ` ` `  `        ``// Numerator value ` `        ``o = o * (o + 2); ` ` `  `        ``// Denominator value ` `        ``e = e * (e + 2); ` `    ``} ` `    ``cout << setprecision(10) << sum; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``double` `x = -0.5; ` ` `  `    ``if` `(``abs``(x) >= 1) { ` `        ``cout << ``"Invalid Input\n"``; ` `        ``return` `0; ` `    ``} ` ` `  `    ``int` `n = 8; ` `    ``find_Solution(x, n); ` `    ``return` `0; ` `} `

## Java

 `//Java implementation of the approach ` `import` `java.io.*; ` ` `  `class` `GFG  ` `{ ` ` `  `// Function to find the arcsin(x) ` `static` `void` `find_Solution(``double` `x, ``int` `n) ` `{ ` `    ``double` `sum = x, e = ``2``, o = ``1``, p = ``1``; ` `    ``for` `(``int` `i = ``2``; i <= n; i++)  ` `    ``{ ` ` `  `        ``// The power to which 'x' is raised ` `        ``p += ``2``; ` ` `  `        ``sum += (``double``)(o / e) *  ` `               ``(``double``)(Math.pow(x, p) / p); ` ` `  `        ``// Numerator value ` `        ``o = o * (o + ``2``); ` ` `  `        ``// Denominator value ` `        ``e = e * (e + ``2``); ` `    ``} ` `    ``System.out.println (sum); ` `} ` ` `  `// Driver code ` `public` `static` `void` `main (String[] args)  ` `{ ` `    ``double` `x = -``0.5``; ` ` `  `    ``if` `(Math.abs(x) >= ``1``) ` `    ``{ ` `        ``System.out.println (``"Invalid Input"``); ` `    ``} ` `     `  `    ``int` `n = ``8``; ` `    ``find_Solution(x, n); ` `} ` `} ` ` `  `// This code is contributed by ajit `

## Python3

 `# Python3 implementation of the approach ` ` `  `# Function to find the arcsin(x) ` `def` `find_Solution(x, n): ` `    ``Sum` `=` `x ` `    ``e ``=` `2` `    ``o ``=` `1` `    ``p ``=` `1` `    ``for` `i ``in` `range``(``2``, n ``+` `1``): ` ` `  `        ``# The power to which 'x' is raised ` `        ``p ``+``=` `2` ` `  `        ``Sum` `+``=` `(o ``/` `e) ``*` `(``pow``(x, p) ``/` `p) ` ` `  `        ``# Numerator value ` `        ``o ``=` `o ``*` `(o ``+` `2``) ` ` `  `        ``# Denominator value ` `        ``e ``=` `e ``*` `(e ``+` `2``) ` `    ``print``(``round``(``Sum``, ``10``)) ` ` `  `# Driver code ` `x ``=` `-``0.5` ` `  `if` `(``abs``(x) >``=` `1``): ` `    ``print``(``"Invalid Input\n"``) ` ` `  `n ``=` `8` `find_Solution(x, n) ` ` `  `# This code is contributed by Mohit Kumar `

## C#

 `// C# implementation of the approach ` `using` `System; ` `class` `GFG  ` `{ ` ` `  `// Function to find the arcsin(x) ` `static` `void` `find_Solution(``double` `x, ``int` `n) ` `{ ` `    ``double` `sum = x, e = 2, o = 1, p = 1; ` `    ``for` `(``int` `i = 2; i <= n; i++)  ` `    ``{ ` ` `  `        ``// The power to which 'x' is raised ` `        ``p += 2; ` ` `  `        ``sum += (``double``)(o / e) *  ` `               ``(``double``)(Math.Pow(x, p) / p); ` ` `  `        ``// Numerator value ` `        ``o = o * (o + 2); ` ` `  `        ``// Denominator value ` `        ``e = e * (e + 2); ` `    ``} ` `    ``Console.WriteLine(sum); ` `} ` ` `  `// Driver code ` `public` `static` `void` `Main (String[] args)  ` `{ ` `    ``double` `x = -0.5; ` ` `  `    ``if` `(Math.Abs(x) >= 1) ` `    ``{ ` `        ``Console.WriteLine(``"Invalid Input"``); ` `    ``} ` `     `  `    ``int` `n = 8; ` `    ``find_Solution(x, n); ` `} ` `} ` ` `  `// This code is contributed by PrinciRaj1992 `

Output:

```-0.5233948501
```

My Personal Notes arrow_drop_up Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.

Article Tags :
Practice Tags :

Be the First to upvote.

Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.