Summing a sequence of fractions to a limit n
I'm wondering if there's anything I can do for the edge case of n = 1?


Yes, I think you are considering it to much (see below: you can simply remove some branching)


  Also, looking at the types for each value, I'm wondering if I need to think more about the data types I chose to use, in terms of should I use a double for this, or an int?.


I think your current choice is fine: int for the denominator and double for the accumulator.



Following your program (my comments adress the previous block of code):

public static void sequenceSum(double n){
    if(n &gt; 1.0){


I think you can simply remove this first condition (already well managed in the while loop)

        int denominator = 1;
        double accumulator = 0;
        System.out.print("1");
        while(accumulator &lt; n) {
            accumulator += ( 1.0 / denominator);
            if(denominator &gt; 1.0){


Your denominator is an int: you should compare it with 1 (and not 1.0)

                System.out.print(" + " + 1 + "/" + denominator);


You should integrate the 1 into the string: " + 1/".

            }
        denominator++;        
        }
    System.out.printf(" = %1.3f", accumulator);
    } else if(n == 1.0){


This branch can simply be replaced with a condition at the very beginning to check if n &lt; 1.0 and immediately return if it is the case.

        System.out.print("1 = 1.000");
    }
}


Miscellaneous

Instead of printing each time, you could append to a StringBuffer 

You have good variable names, except for n. Maybe sumLimit is more appropriate? (or accumulatorLimit).

Simplifying &gt; 1 conditions

You could start your denominator at 2 and your accumulator at 1.0, to get rid of the if condition inside your while loop (if n is 1.0, then the while loop will simply not be executed at all).