Find the Sum of the series 1 + 1/3 + 1/5 + 1/7 + ... till N terms

25 Nov, 2021
Given a number N, the task is to find the sum of the below series till N terms. 
Examples:  
Input: N = 10 Output: 2.133256 Explanation: The sum of series 1 + 1/3 + 1/5 + 1/7 + 1/9 + 1/11 is 2.133256.Input: N = 20 Output: 2.479674 Explanation: The sum of series 1 + 1/3 + 1/5 + 1/7 + ... + 1/41 is 2.479674.  
 
Approach: From the given series, find the formula for Nth term:  
1st term = 1
2nd term = 1/3
3rd term = 1/5
4th term = 1/7
.
.
Nthe term = 1 / (2 * N - 1))
Therefore:  
Nth term of the series 
*** QuickLaTeX cannot compile formula:
 

*** Error message:
Error: Nothing to show, formula is empty

Then iterate over numbers in the range [1, N] to find all the terms using the above formula and compute their sum.Below is the implementation of the above approach:  
C++
Java
Python3
C#
Javascript
// C++ program to find the sum of the// series 1 + 1/3 + 1/5 + ... #include <iostream>using namespace std; // Function to find the sum of the// given seriesvoid printSumSeries(int N){    // Initialise the sum to 0    float sum = 0;     for (int i = 1; i <= N; i++) {         // Generate the ith term and        // add it to the sum        sum += 1.0 / (2 * i - 1);    }     // Print the final sum    cout << sum << endl;} // Driver Codeint main(){    int N = 6;     printSumSeries(N);    return 0;}
// Java program to find the sum of the// series 1 + 1/3 + 1/5 + ...class GFG {         // Function to find the sum of the    // given series    static void printSumSeries(int N)    {        // Initialise the sum to 0        float sum = 0;             for (int i = 1; i <= N; i++) {                 // Generate the ith term and            // add it to the sum            sum += 1.0 / (2 * i - 1);        }             // Print the final sum        System.out.println(sum);    }         // Driver Code    public static void main (String[] args)    {        int N = 6;             printSumSeries(N);     }     } // This code is contributed by AnkitRai01
# Python3 program to find the sum of the# series 1 + 1/3 + 1/5 + ... # Function to find the sum of the# given seriesdef printSumSeries(N) :     # Initialise the sum to 0    sum = 0;     for i in range(1, N + 1) :         # Generate the ith term and        # add it to the sum        sum += 1.0 / (2 * i - 1);     # Print the final sum    print(sum); # Driver Codeif __name__ == "__main__" :     N = 6;     printSumSeries(N); # This code is contributed by AnkitRai01
// C# program to find the sum of the// series 1 + 1/3 + 1/5 + ...using System; class GFG {         // Function to find the sum of the    // given series    static void printSumSeries(int N)    {        // Initialise the sum to 0        float sum = 0;             for (int i = 1; i <= N; i++) {                 // Generate the ith term and            // add it to the sum            sum += (float)1.0 / (2 * i - 1);        }             // Print the final sum        Console.WriteLine(sum);    }         // Driver Code    public static void Main (string[] args)    {        int N = 6;             printSumSeries(N);    }   } // This code is contributed by AnkitRai01
<script> // javascript program to find the sum of the// series 1 + 1/3 + 1/5 + ...  // Function to find the sum of the// given seriesfunction printSumSeries( N){    // Initialise the sum to 0    let sum = 0;     for (let i = 1; i <= N; i++) {         // Generate the ith term and        // add it to the sum        sum += 1.0 / (2 * i - 1);    }     // Print the final sum   document.write(sum.toFixed(5));} // Driver Code     let N = 6;     printSumSeries(N);     // This code is contributed by todaysgaurav  </script>
1.87821
 
Time Complexity: O(N)
Auxiliary Space: O(1)
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