Summation this Summer!

Algebra Level 3

1(1+x)(1+2x)+1(1+2x)(1+3x)+1(1+3x)(1+4x)+\large \dfrac{1}{(1+x)(1+2x)}+\dfrac{1}{(1+2x)(1+3x)}+\dfrac{1}{(1+3x)(1+4x)} + \cdots

Find the closed form of the sum of the series above up to nn terms.

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