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2/3*6 + 2*5/3*6*9 + ... + 2*5*...*2015/3*6...*2019

Source: Saint Petersburg MO 2020 Grade 11 Problem 4

May 7, 2020
number theory

Problem Statement

The sum 23⋅6+2⋅53⋅6⋅9+…+2⋅5⋅…⋅20153⋅6⋅9⋅…⋅2019\frac{2}{3\cdot 6} +\frac{2\cdot 5}{3\cdot 6\cdot 9} +\ldots +\frac{2\cdot5\cdot \ldots \cdot 2015}{3\cdot 6\cdot 9\cdot \ldots \cdot 2019} is written as a decimal number. Find the first digit after the decimal point.
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