Question

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1/1.2.3+1/2.3.4+1/3.4.5+...+1/27.28.29+1/28.29.30

Answer 1

\(=\dfrac{1}{3}.\left(\dfrac{1}{1.2.3}-\dfrac{1}{2.3.4}+\dfrac{1}{2.3.4}-\dfrac{1}{3.4.5}+...+\dfrac{1}{27.28.29}-\dfrac{1}{28.29.30}\right)\)

\(=\dfrac{1}{3}.\left(\dfrac{1}{1.2.3}-\dfrac{1}{28.29.30}\right)\)

\(=\dfrac{1353}{8120}\)