Question
Show that \sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\cdots \infty } } } } = 2 when the layers of square root go to infinite
Show that \sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\cdots \infty } } } } = 2 when the layers of square root go to infinite
Let
when the layers of square root go to infinite
which makes no difference starting to count from the second square root.
Then, we get the following equation
Then,
Square both sides results in a quadratic equation
Factor the left hand side
Then,
or
In summary,