In my previous post(Heuristic-math-problem-solving-skill), I asked the readers to find the sum of the first $n$ terms for the series:
$1+2(1-x)+3(1-x)(1-2x)+4(1-x)(1-2x)(1-3x)+\cdots+n(1-x)(1-2x)\cdots(1-(n-1)x)$
This is one really hard math Olympiad contest problem, but fortunately logical thinking and heuristic problem solving skills are something that we can teach.