HK-PC 2017 Problem 5

Find the first digit after the decimal point of the number $\frac1{1009}+\frac1{1010}+\cdots + \frac1{2016}$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.