TR-MO-R1 2012 Problem 34

$n \geq 2012$ olmak üzere, $1 \cdot 2^1 + 2 \cdot 2^2 + 3 \cdot 2^3 + \cdots + n \cdot 2^n$ sayısının 10 ile bölünmesini sağlayan en küçük $n$ tam sayısı nedir?

a) 2012 b) 2013 c) 2014 d) 2015 e) 2016

Official text Turkish Mathematical Olympiad, first round 2012 official paper, page 10. Quoted with source.

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