Math Gold Medalist

Lor

2014 AIME II 

Problem 7

Let $f(x)=(x^2+3x+2)^{\cos(\pi x)}$. Find the sum of all positive integers $n$ for which $\left |\sum_{k=1}^n\log_{10}f(k)\right|=1.$

Telescoping Rule

Logarithm Rules

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   Solution