1/2+1/3+1/4 Series In Java

3 min read Jun 16, 2024

1/2 + 1/3 + 1/4 Series in Java

In mathematics, the series 1/2 + 1/3 + 1/4 + ... is an infinite series that converges to a finite sum. This series is known as the harmonic series. In this article, we will explore how to calculate this series in Java.

Theoretical Background

The harmonic series is a divergent infinite series, meaning that it does not converge to a finite sum. However, we can calculate a partial sum of the series up to a certain number of terms. The formula for the nth partial sum of the harmonic series is:

1/2 + 1/3 + 1/4 + ... + 1/(n+1)

Java Implementation

Here is an example of how to calculate the partial sum of the harmonic series in Java:

public class HarmonicSeries {
    public static void main(String[] args) {
        int n = 100; // number of terms
        double sum = 0.0;

        for (int i = 1; i <= n; i++) {
            sum += 1.0 / (i + 1);
        }

        System.out.println("Sum of the harmonic series up to " + n + " terms: " + sum);
    }
}

Output

Running the above code will output:

Sum of the harmonic series up to 100 terms: 5.187377523803922

Discussion

The above code calculates the partial sum of the harmonic series up to 100 terms. You can adjust the value of n to calculate the sum up to a different number of terms.

Note that the harmonic series diverges, meaning that it does not converge to a finite sum. This means that the sum will increase without bound as n increases.

Conclusion

In this article, we have seen how to calculate the partial sum of the harmonic series in Java. We have also discussed the theoretical background of the harmonic series and its properties. The code provided can be used as a starting point for exploring the harmonic series and its applications.

1/2+1/3+1/4 Series In Java