Is there a way to display the stack during recursion method?

You cannot access the stack contents directly from your Java code, but if you use a debugger (which is integrated in every modern IDE) you get something even better: it will list the stack of method calls and for each level, if you select it, the values of the local variables on the stack.

Here's a tutorial on how to use the debugger in eclipse.

You can use a debugger like eclipse to view the stack at any given time, but trying to envision recursion as a loop isn't the best way to understand it. As you go down the stack, you break off small pieces of the problem, until you get to the bottom of the stack, where the problem is trivial to solve. Then as you go back up the stack, you put the pieces back together again.

sum(4)
sum(3) + 4
sum(2) + 3
sum(1) + 2
1

sum(4) is broken down into sum(3) + 4. sum(3) is broken down into sum(2) + 3. Eventually you get to sum(1), which has a trivial answer of 1 (the first choice in your if statement).

There's no possible way to break it down further, so you go back up the stack, adding 2, 3, and 4. It's a ride down and up the stack, a very different thing from a loop, even though they can accomplish the same calculation.

You can access the stack, but not the values on the stack.

public class StackTrace {

    public static void main(String[] args) {
        recurse(10);
    }

    static void recurse(int depth) {
        for (StackTraceElement each: new Exception().getStackTrace()) System.out.println(each);
        if (depth > 0) recurse(depth - 1);
    }

}

Of course we could also write a program that maintains its own, C style, stack, where we push all arguments and locals and return values on the stack

public class Main {

    public static void main(String[] args) {
        new Main().run();
    }

    int[] stack = new int[100];
    int base = 0;

    public void run() {

        // push arguments on stack
        stack[base] = 4;
        // increase base pointer and call method
        base += 1;
        call();
        // retrieve result
        int result = stack[base];
        // print it
        System.out.println(result);

    }

    public void call() {
        // push locals on stack and increase base, now arg n
        // is at base - 2 and local sum is at base - 1
        stack[base] = 0;
        base += 1;
        // test if n equals 1
        if (stack[base - 2] == 1) {
            // if yes set sum to 1
            stack[base - 1] = 1;
        } else {
            // push new argument on stack
            stack[base] = stack[base - 2] - 1;
            // increase base pointer and call method
            base += 1;
            call();
            // add result to sum
            stack[base - 1] += stack[base];
            // add n to sum
            stack[base - 1] += stack[base - 2];
        }
        // cache return value
        int result = stack[base - 1];
        // decrease base pointer by size of both args and locals
        base -= 2;
        // push result on stack
        stack[base] = result;
    }
}

the programs uses the calling convention that callers are responsible for pushing arguments and increasing the base pointers, and receivers are responsible for resetting the base pointer and leaving a return value on the stack.

This is how method calls happen at the machine level.