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Magazine Problem 13
Find the radius of convergence \(R\) and interval of convergence for \(\sum a_{n} x^{n}\) with the given coefficients \(a_{n}\). $$ \sum_{n=1}^{\infty} \frac{(2 x)^{n}}{n} $$
Problem 14
Find the radius of convergence \(R\) and interval of convergence for \(\sum a_{n} x^{n}\) with the given coefficients \(a_{n}\). $$ \sum_{n=1}^{\infty}(-1)^{n} \frac{x^{n}}{\sqrt{n}} $$
Problem 15
Find the radius of convergence \(R\) and interval of convergence for \(\sum a_{n} x^{n}\) with the given coefficients \(a_{n}\). $$ \sum_{n=1}^{\infty} \frac{n x^{n}}{2^{n}} $$
Problem 16
Find the radius of convergence \(R\) and interval of convergence for \(\sum a_{n} x^{n}\) with the given coefficients \(a_{n}\). $$ \sum_{n=1}^{\infty} \frac{n x^{n}}{e^{n}} $$
Problem 17
Find the radius of convergence \(R\) and interval of convergence for \(\sum a_{n} x^{n}\) with the given coefficients \(a_{n}\). $$ \sum_{n=1}^{\infty} \frac{n^{2} x^{n}}{2^{n}} $$
Problem 18
Find the radius of convergence \(R\) and interval of convergence for \(\sum a_{n} x^{n}\) with the given coefficients \(a_{n}\). $$ \sum_{k=1}^{\infty} \frac{k^{e} x^{k}}{e^{k}} $$
Problem 19
Find the radius of convergence \(R\) and interval of convergence for \(\sum a_{n} x^{n}\) with the given coefficients \(a_{n}\). $$ \sum_{k=1}^{\infty} \frac{\pi^{k} x^{k}}{k^{\pi}} $$
Problem 20
Find the radius of convergence \(R\) and interval of convergence for \(\sum a_{n} x^{n}\) with the given coefficients \(a_{n}\). $$ \sum_{n=1}^{\infty} \frac{x^{n}}{n !} $$
Problem 21
Find the radius of convergence \(R\) and interval of convergence for \(\sum a_{n} x^{n}\) with the given coefficients \(a_{n}\). $$ \sum_{n=1}^{\infty} \frac{10^{n} x^{n}}{n !} $$
Problem 22
Find the radius of convergence \(R\) and interval of convergence for \(\sum a_{n} x^{n}\) with the given coefficients \(a_{n}\). $$ \sum_{n=1}^{\infty}(-1)^{n} \frac{x^{n}}{\ln (2 n)} $$
