HMMT 1998 V3

Find the sum of the infinite series

$1+2\left(\frac{1}{1998}\right)+3\left(\frac{1}{1998}\right)^{2}+4\left(\frac{1}{1998}\right)^{3}+\ldots$

Dataset text NuminaMath olympiads. Quoted with source.

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\left(\frac{1998}{1997}\right)^{2}

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