A series is given by $\frac{1}{{{\log }_{3}}x}+\frac{1}{{{\log }_{{{3}^{3}}}}x}+\frac{1}{{{\log }_{{

Question

A series is given by $\frac{1}{{{\log }_{3}}x}+\frac{1}{{{\log }_{{{3}^{3}}}}x}+\frac{1}{{{\log }_{{{3}^{5}}}}x}+\ldots +\frac{1}{{{\log }_{{{3}^{2n-1}}}}x}$ where $n\in {{\mathbb{Z}}^{+}}$. If the sum of the first thirty terms is at least $300$, show that $\frac{3\ln 3}{\ln x}\ge 1$.

Accepted Answer

$\frac{3\ln 3}{\ln x} \geq 1$

2012 AJC FE Q2

2012 AJC FE Q2

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