다음 부등식을 증명하여라.
(1) $\frac {43}{44} < \frac 1{\sqrt 2+2}+\frac 1{2\sqrt 3+3\sqrt 2}+\cdots +\frac 1{1988\sqrt{1989}+1989\sqrt{1988}} < \frac {44}{45}$
(2) $\frac {1\cdot 3\cdot 5\cdots (2n-1)}{2\cdot 4\cdot 6\cdots (2n)} <\frac 1{\sqrt {2n}}\qquad (n\ge 1)$.