X 1 equals the square root of 6, and xn plus 1 equals xn under the root sign of 6. It is easy to prove that the square root of 6 is less than or equal to xn and less than or equal to 3 by mathematical
X 1 equals the square root of 6, and xn plus 1 equals xn under the root sign of 6. It is easy to prove that the square root of 6 is less than or equal to xn and less than or equal to 3 by mathematical induction. How to prove it specifically? Thank you for your answers.
Induction:
X2=√﹙6+√6﹚
X3=√﹙6﹢√﹙6﹢√6﹚﹚
..
Xn=√6﹢√﹙6﹢……√﹙6﹢√﹙6+√6﹚﹚﹚
Xn>√6
√6