copy paste this into a javascript shell and you'll get 33.33333333333333

brute force limit folding a paper

var lim = function (num) {
    if (num === void 0) num = 100;

    var series = [100, 50, 25];
    var next = function () {
        var lastTerm = series[series.length - 1];
        var secondToLastTerm = series[series.length - 2];

        // notice that, since we started above with the first three terms, that the fliping back and forth between adding
        // and subtracting is handled here ↓, i.e. `secondToLastTerm - lastTerm` is alternating negative and positive
        var nextValue = lastTerm + ((secondToLastTerm - lastTerm) / 2);

        series.push(nextValue);
    }

    for (var i = 0; i < num; i++) {
        next();
    }

    return series[series.length - 1];
};

lim(1000);