$3P = \dfrac{3}{1.2.3.4}+\dfrac{3}{2.3.4.5}+...+\dfrac{1}{97.98.99.100}$

$3P = \dfrac{1}{1.2.3}-\dfrac{1}{2.3.4}+\dfrac{1}{2.3.4}-\dfrac{1}{3.4.5}+...+\dfrac{1}{97.98.99}-\dfrac{1}{98.99.100}$

$3P = \dfrac{1}{1.2.3}-\dfrac{1}{98.99.100}$

$3P = \dfrac{1}{6}-\dfrac{1}{970200}$

$3P = \dfrac{161700}{970200}-\dfrac{1}{970200}$

$3P = \dfrac{161699}{970200}$

$P = \dfrac{161699}{970200} : 3$

$P = \dfrac{161699}{200600}$

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