Ascertain the value of the limit (if it exists): \(\lim \sum\limits_{k = 0}^{2n} {2^{ - k} \cos \sqrt {\frac{k}{n}} } \) HINT: If you were able to follow the proofs to the problem Convergent sequence 2 then you can place this at the slightly advanced high school level (say AP Calculus BC).
My intuition tells me pretty strongly that the answer is 2, but I can attempt a rigorous proof later on.
