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++ 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 series 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
cout << sum << endl;
} // Driver Code int 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 series def 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 Code if __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 series function 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> |
Output:
1.87821
Time Complexity: O(N)
Auxiliary Space: O(1), since no extra space has been taken.