1. Pure Mathematics 1

Sequences Series — Quiz

Test your understanding of sequences series with 5 practice questions.

Practice Questions

Question 1

What is the nth term a_n if the sum of the first n terms is S_n = n^3 + 2n^2 - n?

Question 2

What is the sum to infinity of the series $\sum_{n=1}^{\infty}\frac{2^n}{3^{n+1}}$?

Question 3

Does the series $\sum_{n=1}^{\infty}\frac{n!}{n^n}$ converge or diverge?

Question 4

What is the sum $\sum_{k=1}^n\frac{1}{k(k+1)}$?

Question 5

For the geometric sequence $a_n=5\bigl(\tfrac{3}{4}\bigr)^{n-1}$, what is the smallest integer $n$ such that $a_n<0.1$?