what i'm i doing wrong on this algorithm?

Question

I've been stuck on this code for a couple of hours. The sum is S = 1-x + x^2 - x^3 + x^4.
We ask for X and N with starting value of i = 0. Whenever the previous exponent (i) is odd we add x^i, and if the previous exponent is even we subtract x^i.
I've put them on a loop but i can't seem to get the sum correctly. Can anyone tell me what I'm doing wrong? Thank you!

import java.util.Scanner;

public class hw1 {
    public static void main(String[] args) {
        try (Scanner scan = new Scanner(System.in)) {
            System.out.println("Sum = 1^0-x^1+x^2-x^3..+x^n");
            System.out.println("Enter number X");
            int X = scan.nextInt();
            System.out.println("Enter number N");
            int N = scan.nextInt();
            int sum = 0;
            for (int i = 0; i <= N; i++) {
                if (i < N) {
                    if (i % 2 != 0)    // if I is even 
                    {
                        sum = sum - (X ^ i);
                    } else    // if I is odd 
                    {
                        sum = sum + (X ^ i);
                    }
                }
            }
            System.out.println("Z is " + sum);
        }
    }
}

Answer 1

So I fixed a few things in your code:

1. I switched the ^ operator (which, as @Nick Bell pointed out, is a bitwise exclusive OR) for Math.pow.
2. I fixed the spelling of your variables x and n. In Java, convention is to give variables names that start with lower-case. Upper-cases (X and N) are reserved for constants (fields marked final) and for classes (as opposed to objects). Note that this is only a convention, and that the code works fine both ways. It just helps in reading the code.
3. Your odd/even check was inverted: x % 2 == 0 is true for even numbers.
4. The reason that you inverted your odd/even check was probably the two operations on sum were inverted. Compare with the description of your problem in the first paragraph of your question, you'll see where you went wrong.
5. The if i < N check was redundant. It you really wanted to limit computation to i < N, you should specify it directly in your first for loop.
6. I added two try/catch blocks with infinite loops that break when an integer is entered, because your previous code threw an exception and stopped if you entered something else than a well-formed integer (such as letters, or a decimal value). Up to you to keep them or delete them.
7. By the way, initializing x and n to 0 is now redundant, since your code is guaranteed to assign them another value right away.

This is the updated code.

public static void main(String[] args) {
    try (Scanner scan = new Scanner(System.in)) {
        System.out.println("Sum = 1^0-x^1+x^2-x^3..+x^n");
        System.out.println("Enter number X");
        int x = 0;
        while (true) {
            try {
                x = Integer.parseInt(scan.nextLine());
                break;
            } catch (NumberFormatException e) {
                System.out.println("Enter an integer.");
            }
        }
        System.out.println("Enter number N");
        int n = 0;
        while (true) {
            try {
                n = Integer.parseInt(scan.nextLine());
                break;
            } catch (NumberFormatException e) {
                System.out.println("Enter an integer.");
            }
        }
        double sum = 0;
        for (int i = 0; i <= n; i++) {
            if (i % 2 == 0)    // if I is even
                sum = sum + Math.pow(x, i);
            else    // if I is odd
                sum = sum - Math.pow(x, i);
        }
        System.out.println("Z is " + sum);
    }
}