6.(Tricky Problem)
$2\sqrt{k} < \sqrt{k}+\sqrt{k+1} < 2\sqrt{k+1}$
$\dfrac{1}{2\sqrt{k}} < \sqrt{k+1}-\sqrt{k} < \dfrac{1}{2\sqrt{k+1}}$
10.
$\cos 36^\circ-\cos 72^\circ = 2\sin (-18^\circ)\sin 54^\circ$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =-2\sin 18^\circ\cos 36^\circ$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =\dfrac{-4\sin 18^\circ\cos 18^\circ\cos 36^\circ}{2\cos 18^\circ}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \dfrac{-\sin 72^\circ}{ 2\cos 18^\circ}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = -\dfrac{1}{2}$