Find the limit of $(\sqrt2-\root3\of2 )(\sqrt2 -\root4\of2 )...(\sqrt 2-\root{n}\of2 )$ without using the squeezing principle
Finding the limit of roots products $(\sqrt{2}-\sqrt[3]{2})(\sqrt{2}-\sqrt[4]{2})(\sqrt{2}-\sqrt[5]{2})\cdot \cdot \cdot (\sqrt{2}-\sqrt[n]{2})$