解:
(1)$\because(ab - 2)^2\geq0,$$\sqrt{b - 1}\geq0,$$(ab - 2)^2+\sqrt{b - 1}=0,$$\therefore ab - 2 = 0,$$b - 1 = 0,$$\therefore a = 2,$$b = 1。$
(2)當(dāng)$a = 2,$$b = 1$時(shí),原式$=\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+\cdots+\frac{1}{2025\times2026}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\cdots+\frac{1}{2025}-\frac{1}{2026}=1-\frac{1}{2026}=\frac{2025}{2026}。$