已知正项数列\(\{a_{n}\}\)满足\(a_{1}=1\)，\((\dfrac{1}{a_{n+1}}+\dfrac{1}{a_{n}})(\dfrac{1}{a_{n+1}}-\dfrac{1}{a_{n}})=4\)，数列\(\{b_{n}\}\)满足\(\dfrac{1}{b_{n}}=\dfrac{1}{a_{n+1}}+\dfrac{1}{a_{n}}\)，记\(\{b_{n}\}\)的前\(n\)项和为\(T_{n}\)，则\(T_{20}\)的值为 ______ .