5．
观察等式：\(\dfrac{1}{1\times 3}=\dfrac{1}{2}(\dfrac{1}{1}-\dfrac{1}{3})\)，\(\dfrac{1}{3\times 5}=\dfrac{1}{2}(\dfrac{1}{3}-\dfrac{1}{5})\)，\(\dfrac{1}{5\times 7}=\dfrac{1}{2}(\dfrac{1}{5}-\dfrac{1}{7})\)，你发现的规律计算：\(\dfrac{1}{1\times 3}+\dfrac{1}{3\times 5}+\dfrac{1}{5\times 7}+\cdots +\dfrac{1}{(2n-1)(2n+1)}={ }\!\!\_\!\!{ }\!\!\_\!\!{ }\!\!\_\!\!{ }\!\!\_\!\!{ }\!\!\_\!\!{ }\!\!\_\!\!{ }\!\!\_\!\!{ }\!\!\_\!\!{ }.(n\)为正整数\()\)