Find the sum of N terms of the series 1/1*3, 1/3*5, 1/5*7, ....

Given a positive integer, N. Find the sum of the first N term of the series-

1/1*3, 1/3*5, 1/5*7, ....

Examples:

Input: N = 3

Output: 0.428571

Input: N = 1

Output: 0.333333

Approach: The sequence is formed by using the following pattern. For any value N-

S_N = N / (2 * N + 1)

Below is the implementation of the above approach:

// C++ program to implement
// the above approach

#include <bits/stdc++.h>
using namespace std;

// Function to return sum of
// N term of the series

double findSum(int N) {
  return (double)N / (2 * N + 1); 
}

// Driver Code

int main()
{
    int N = 3;

    cout << findSum(N);
}

// JAVA program to implement
// the above approach
import java.util.*;
class GFG 
{

  // Function to return sum of
  // N term of the series
  public static double findSum(int N)
  {
    return (double)N / (2 * N + 1);
  }

  // Driver Code
  public static void main(String[] args)
  {
    int N = 3;

    System.out.print(findSum(N));
  }
}

// This code is contributed by Taranpreet

# Python 3 program for the above approach

# Function to return sum of
# N term of the series

def findSum(N):
  return N / (2 * N + 1)


# Driver Code
if __name__ == "__main__":
  
    # Value of N
    N = 3    
    print(findSum(N))

# This code is contributed by Abhishek Thakur.

// C# program to implement
// the above approach
using System;
class GFG
{

  // Function to return sum of
  // N term of the series
  public static double findSum(int N)
  {
    return (double)N / (2 * N + 1);
  }

  // Driver Code
  public static void Main()
  {
    int N = 3;

    Console.Write(findSum(N));
  }
}

// This code is contributed by gfgking

<script>
// Javascript program to implement
// the above approach

// Function to return sum of
// N term of the series

function findSum(N) {
  return N / (2 * N + 1); 
}

// Driver Code

let N = 3;

document.write(findSum(N));

// This code is contributed by Palak Gupta
</script>

0.428571

 Time Complexity: O(1), since there is no loop or recursion.
Auxiliary Space: O(1), since no extra space has been taken.