<p>Let <img alt="$f(x)=(x^2+3x+2)^{\cos(\pi x)}$" height="20" src="https://latex.artofproblemsolving.com/2/8/9/2894b6e6d190ad90565c29048a4fb1cd0c50fec2.png" width="207" />. Find the sum of all positive integers <img alt="$n$" height="8" src="https://latex.artofproblemsolving.com/1/7/4/174fadd07fd54c9afe288e96558c92e0c1da733a.png" width="10" /> for which       <img alt="\[\left |\sum_{k=1}^n\log_{10}f(k)\right|=1.\]" src="https://latex.artofproblemsolving.com/3/8/9/389a540c1dec657ab2e68535a6098d77f575cdcb.png" style="width: 150px; height: 54px;" /></p>

Question No: 385

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

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Tags: Algebra

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