6. Further Pure Mathematics

Further Series — Quiz

Test your understanding of further series with 5 practice questions.

Practice Questions

Question 1

Consider the function series $\sum_{n=1}^\infty \frac{x^n}{n}$ on the interval $[0,1)$. Which statement about its convergence is correct?

Question 2

Use the ratio test to determine the radius of convergence $R$ for the power series $\sum_{n=0}^\infty \frac{(n+1)(x-2)^n}{5^n}$.

Question 3

Find the interval of convergence of the power series $\sum_{n=1}^\infty \frac{x^n}{n\,2^n}$ including endpoint behavior.

Question 4

Use the root test to find the radius of convergence $R$ for the series $\sum_{n=1}^\infty \frac{n^n\,x^n}{n!}$.

Question 5

Which test is most appropriate to show that the power series $\sum_{n=0}^\infty \frac{x^{2n}}{(2n)!}$ converges uniformly on every closed interval $[-A,A]$?