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tail recursion practice

Convert the following loop to a tail-recursive version (both in Java ¹, and then in racket). Emphasize the similarities -- your functions should use the same-named variables to compute the same answer in the exact same way (e.g. initialize the variables the same way, and update them the same way). It's just that your code won't have a loop-construct like “for” or “while”. Be sure to include a purpose-statement for your helper-function; it should (of course) mention all of its parameters.

class TailRecursionPractice {

    /** @return 2^0 + 2^1 + 2^2 + ... + 2^(n-1). */
    static long sumPowersOf2( int n ) {
        long sumSoFar = 0L;
        for (int i=0;  i<n;  i=i+1) {
            sumSoFar = sumSoFar + Math.pow(2,i);
            }
        return sumSoFar;
        // Btw: There is a much shorter implementation that you learned in discrete math. What is it?
        }
    }

¹ Though remember that javac doesn't optimize tail-recursive functions (and can't, for backwards-compatibility with exceptions). Howeverk being tail-recursive is an aspect of teh source-code, not the compiler. You might also remember that racket implementations are required by the language-spec to optimize tail-recursive functions — else they're not true implementations. ↩

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