What Will Be the Code for the Series X * x^2 /2 * x^3 /4 * x^4 /7 * x^5 /11 * x^6 /16...n in C and Java?

In this article, we will delve into the implementation of a mathematical series in both C and Java. The series in question is defined as follows:

Sx n x * (x^2 / 2) * (x^3 / 4) * (x^4 / 7) * (x^5 / 11) * (x^6 / 16)...

Understanding the Series

To implement this series in C and Java, the first step is to observe the pattern in the denominators. The denominators follow a specific sequence, which can be defined as the sequence of triangular numbers plus one. Specifically, the sequence of denominators is:

This sequence can be defined recursively, where the kth term in the denominator can be expressed as:

dk dk-1 (k - 1)

Implementation in C

Let's first implement the series in C. The key steps include initializing variables, iterating through the terms of the series, and updating the denominators accordingly.

// Include necessary headersinclude stdio.hinclude math.hdouble series(double x, int n) {    double sum  0.0;    int d  1; // Start with the first denominator    for (int i  1; i // Calculate the current term        // Update the denominator for the next term        if (i  2) {            d  i - 1; // Update d according to the pattern        }    }    return sum;}int main() {    double x;    int n;    // Input from the user    printf("Enter the value of x: ");    scanf("%lf", x);    printf("Enter the number of terms n: ");    scanf("%d", n);    double result  series(x, n);    printf("The result is: %f", result);    return 0;}

Implementation in Java

Now, let's implement the series in Java. The implementation follows a similar approach, with specific attention to Java's syntax and libraries.

@annotation *;
class Pattern {    public static void main(@annotation [] args) throws IOException {        BufferedReader in  new BufferedReader(new InputStreamReader());        char[] buffer  new char[12];        int n  (buffer);        int x  (buffer);        int s  1;        int d  1;        double pdivsum  0.0;        for (int i  0; i  n; i  ) {            d  d   i;            double p  Math.pow(x, i);            s  s   i;            double div  p / s;            pdivsum  pdivsum   div;        }        (pdivsum);    }}

Explanation

The function series in C and the Pattern class in Java are responsible for computing the sum of the series up to n terms. The loop iterates from 1 to n, updating the denominator and multiplying by the current term to get the sum.

Usage

To use this code, compile and run the respective C and Java programs. You will be prompted to enter the values of x and n. The output will be the sum of the series.

Conclusion

This article has provided a detailed explanation and implementation of the series X * x^2 /2 * x^3 /4 * x^4 /7 * x^5 /11 * x^6 /16... in both C and Java. Understanding the recursive pattern in the denominators is crucial for implementing such series efficiently.

By following the steps outlined in this article, you can effectively calculate the desired series using either C or Java. The provided code snippets should serve as a useful starting point for solving similar mathematical series in your programming projects.