[3^(n+1)-1]/(3ⁿ-1)≤(3n+1)/n
n[3^(n+1)-1]≤(3ⁿ-1)(3n+1)
n*3^(n+1)-n≤3n*3ⁿ+3ⁿ-3n-1
3n*3ⁿ-n≤3n*3ⁿ+3ⁿ-3n-1
-n≤3ⁿ-3n-1
3ⁿ≥-n+3n+1=2n+1
3ⁿ≥2n+1