Question

3的n加1次方减去1,除以3的n次方减1,小于等于3n加1除以n .如何化为3的n次方大于等于2n加1,求化简的过程

Answer 1

[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