\(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{99\cdot100}\)
P \(=1-\dfrac{1}{2}-+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{99}+\dfrac{1}{99}-\dfrac{1}{100}\)
P \(=1-\dfrac{1}{100}\)
P \(=\dfrac{100}{100}-\dfrac{1}{100}\)
P \(=\dfrac{99}{100}\)