Evaluate the following expression to 4 decimal places:
where the number of square roots in the expression is exactly 2015.
As per the no-computers tag, you may not use a computer, calculator, or any electronic aid in your calculations. You may look up the decimal expansion of a certain constant, but the people answering this question will probably have it memorised to several decimal places anyway!
I believe I found this puzzle somewhere on the internet, rather than having made it up myself, but after such a long time I can't remember where. If anyone finds this puzzle elsewhere on the web, please drop a link in a comment and I'll edit it in.