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SMO 2026 Open Round 1 Question 10

SMO · SMO 2026 Open Round 1

Question 10

Let $f(x)=\frac{9^x}{9^x+3}$. If $$m=f\left(\frac1{2026}\right)+f\left(\frac2{2026}\right)+\cdots+f\left(\frac{2025}{2026}\right),$$ find the value of $\lfloor2m\rfloor$.