) We have seen that the harmonic series: \sum_{n=1}^{\infty} \frac{1}{n}=1+\frac{1}{2}+\frac{1}{3}+\cdots+\frac{1}{n}+\cdots is divirgent. Is the series \sum_{n=1}^{\infty} \frac{1}{2 n-1}=1+\frac{1}{3}+\frac{1}{5}+\cdots+\frac{1}{2 n-1}+\cdots i.e. the harmonic series with every second term removed, convergent or divirgent? Prove your answer. (b) Determine the radius of convergence and the interval of convergence for the power series: \sum_{n=1}^{\infty} \frac{(-1)^{n} n}{5^{n}}(x+3)^{n} (c) Find a power series representation of the function: f(x)=\frac{1}{1+3 x} Hence (or otherwise) find the power series representation of the function: g(x)=\log (\sqrt[3]{1+3 x}) What is the radius of convergence of the power series representation of g(x)?