6. Series and Sequences

Series Introduction — Quiz

Test your understanding of series introduction with 5 practice questions.

Practice Questions

Question 1

For a series $ \sum_{n=1}^{\infty} a_n $, if the sequence of partial sums $ S_n $ converges to a limit $ L $, what is the value of $ \lim_{n \to \infty} a_n $?

Question 2

Consider the series $ \sum_{n=1}^{\infty} \frac{1}{n(n+1)} $. What is the $ n^{th} $ partial sum, $ S_n $?

Question 3

Which of the following statements is true about the convergence of the series $ \sum_{n=1}^{\infty} \frac{1}{\sqrt{n}} $?

Question 4

If a series $ \sum_{n=1}^{\infty} a_n $ converges, and $ S_n $ is its $ n^{th} $ partial sum, what can be said about the sequence $ \{S_n\} $?

Question 5

Consider the series $ \sum_{n=1}^{\infty} \left( \frac{1}{2} \right)^{n-1} $. What is the sum of this infinite series?