Addition of Fractions in a Loop

Question

I was assigned an assignment where I have to create a program to add the following numbers and then tell the user the answer while using a loop statement.

(1/3 + 3/5 + 5/7 + 7/9 + 9/11 + 11/13 + ... 95 / 97 + 97/99) The answer should be 45.12445 according to the professor but I am receiving the answer 40.92541 and I'm having trouble figuring out where the error in my logic is.

public class HW6
public static void main(String[]args)
    {
            //Declarations
            double num;
            double denom;
            double holder1;
            double sum;
            num=1;
            denom = 3;
            sum=0;


            // Perform loop
            for (num=1;num<=98;num=num+2) {
                    num = num+2;
                    denom = denom+2;
                    holder1 = num/denom;
                    sum= sum+holder1;
                    }

            // Print sum
            System.out.println("The sum is " +sum);
    }
}

Answer 1

To understand the problem in your logic, take it one step at a time. Your initialization before the loop looks fine, so let's start at the beginning of the loop:

Iteration 1

for (num=1;num<=98;num=num+2) {

At this point, your variables contain the following:

num == 1, denom == 3, sum == 0, and holder == undefined (because you didn't initialize it)

After the following statement:

num = num+2;

num changes to 3, so we now have:

num == 3, denom == 3, sum == 0, and holder == undefined.

After the next statement:

denom = denom+2;

denom changes from 3 to 5, so we have:

num == 3, denom == 5, sum == 0, and holder == undefined.

Then, after

holder1 = num/denom;

we have the first calculated fraction, which (since num==3 and denom==5) is 3/5, or 0.6. You will probably notice that this is not what you intended, because according to your assignment the first fraction in the series is supposed to be 1/3. So the first problem with your logic is that you are adding 2 to both num and denom before you calculate the first fraction in the series.

Continuing to step through your code, after

sum= sum+holder1;

the variables contain

num == 3, denom == 5, sum == 0.6, and holder == 0.6.

Iteration 2

Now before looping back to execute the next iteration of the for loop, the num variable will be incremented by 2, as specified by the third expression in your for loop definition: num=num+2. So when the loop begins for the second iteration, the variables contain:

num == 5, denom == 5, sum == 0.6, and holder == 0.6.

As before, the next two statements increment num and denom, respectively, by 2, so before the next fraction is computed, the variables contain:

num == 7, denom == 7, sum == 0.6, and holder == 0.6.

Variable holder is then computed as num/denom = 7/7 = 1.0 (which is certainly not a fraction that is part of the correct series), and after adding this to sum, you have

num == 7, denom == 7, sum == 1.6, and holder == 1.0.

Conclusion

So there are at least two errors in your logic. The first is that after initializing num and denom to 1 and 3, respectively, you add 2 to each before calculating their ratio. What you probably should do instead is add 2 to each of num and denom after you calculate their ratio, but before jumping back to the start of the loop.

The second error, which you hopefully noticed as we stepped through the code, is that you are adding 2 to num twice with each time through the loop: once at the bottom of the loop according to your for specifier, and once at the top of the loop. You only need one of those increment-by-2 operations.

So an improved loop would look like:

        for (num=1;num<=98;num=num+2) {
                holder1 = num/denom;
                sum= sum+holder1;
                denom = denom+2;
                }