Question

If \[a _{1}=\sqrt{2}, a _{2}=\sqrt{2\sqrt{2}}, a _{3}=\sqrt{2\sqrt{2\sqrt{2}}}, a _{4}=\sqrt{2\sqrt{2\sqrt{2\sqrt{2}}}}\] and if a^n is obtained by iterating this process n times, then write a recursive formula for a^n. Once you have the recursive formula assume the limit exists and use it to find the limit