6. Advanced Topics

Series — Quiz

Test your understanding of series with 5 practice questions.

Practice Questions

Question 1

Using the Ratio Test, determine whether the infinite series $\sum_{n=1}^\infty \frac{n^2}{3^n}$ converges or diverges.

Question 2

Evaluate the finite sum $S_n=\sum_{k=1}^n\frac{1}{\sqrt{k}+\sqrt{k+1}}$ in simplified closed form.

Question 3

Given the partial sum $S_n=\frac{n}{n+2}$ for a sequence, find the general term $a_n$.

Question 4

Determine whether the series $\sum_{n=1}^\infty n^{1/n}$ converges or diverges, stating the test used.

Question 5

Which formula gives the sum of the squares of the first $n$ positive integers, $\sum_{k=1}^n k^2$?