An algebra problem by Tan T

Algebra Level 3

\[\dfrac 3{1 \times 2} \left( \dfrac 12 \right) + \dfrac 4{2 \times 3} \left( \dfrac 14 \right) + \dfrac 5{3 \times 4} \left( \dfrac 18 \right) + \cdots \]

Find the sum of the first 9 terms of the summation above.

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