1+1/2+1/3+...+1/n Sum Formula In C

Suzhoumeite

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Jun 15, 2024

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The 1+1/2+1/3+...+1/n Sum Formula in C

The harmonic series is a well-known mathematical concept that has been studied for centuries. The sum of the reciprocals of the positive integers, also known as the harmonic series, is a divergent infinite series. However, we can calculate the sum of the first n terms of the harmonic series, which is a convergent series.

The Formula

The sum of the first n terms of the harmonic series is given by the formula:

$1 + \frac{1}{2} + \frac{1}{3} + ... + \frac{1}{n} = \sum_{k=1}^{n} \frac{1}{k}$

Implementation in C

Here is an example implementation of the formula in C:

#include 

double harmonic_sum(int n) {
    double sum = 0.0;
    for (int k = 1; k <= n; k++) {
        sum += 1.0 / k;
    }
    return sum;
}

int main() {
    int n;
    printf("Enter the number of terms: ");
    scanf("%d", &n);
    double sum = harmonic_sum(n);
    printf("The sum of the first %d terms is: %f\n", n, sum);
    return 0;
}

Explanation

The harmonic_sum function takes an integer n as input and returns the sum of the first n terms of the harmonic series. The function uses a for loop to iterate from 1 to n, adding the reciprocal of each term to the sum.

In the main function, we prompt the user to enter the number of terms n, and then call the harmonic_sum function to calculate the sum. Finally, we print the result to the console.

Example Output

Here is an example output of the program:

Enter the number of terms: 5
The sum of the first 5 terms is: 2.283333

Note that the actual output may vary depending on the value of n entered by the user.

I hope this helps! Let me know if you have any questions.