Sequences and Series — Quiz 1

Questions in this quiz (10)

1. Determine whether or not the sequence $$\left\{\frac{4n^3+3n-2}{7n^3-5n^2+1}\right\}$$ is convergent or divergent.

   • Converges to $$0$$
   • Converges to $$\frac47$$
   • Diverges to infinity
   • Diverges

2. Find the sum of the series $$\sum_{n=1}^{\infty}\left(\frac{1}{n+2}-\frac{1}{n+4}\right)$$.

   • $$\frac12$$
   • $$\frac34$$
   • $$\frac{7}{12}$$
   • $$\frac23$$

3. Determine if the sequence $$\left\{\frac{\ln n}{n}\right\}$$ converges.

   • Converges to $$0$$
   • Converges to $$1$$
   • Diverges
   • Oscillates

4. Find the $$n$$th term and determine convergence for the sequence $$3,\frac32,\frac34,\frac38,\frac{3}{16},\ldots$$.

   • $$a_n=\frac{3}{2^n}$$, converges to $$0$$
   • $$a_n=\frac{3}{n}$$, converges to $$0$$
   • $$a_n=\frac{3}{2n}$$, diverges
   • $$a_n=\frac{3}{2^{n-1}}$$, converges to $$0$$

5. Use the nth-term divergence test to determine whether the series $$\sum_{n=1}^{\infty}\frac{2n^3+1}{5n^3-2n+4}$$ converges.

   • Converges
   • Diverges
   • Conditionally converges
   • Cannot determine

6. What is the sum of $$\sum_{n=1}^{\infty}\left(\frac{1}{n+2}-\frac{1}{n+5}\right)$$?

   • $$\frac{47}{60}$$
   • $$\frac{7}{12}$$
   • $$\frac{11}{12}$$
   • $$\frac56$$

7. Determine whether or not the series converges $$\sum_{n=1}^{\infty}\frac{1}{\sqrt[4]{n^6+2}}$$

   • Converges by comparison test
   • Diverges by p-series test
   • Converges conditionally
   • Diverges by ratio test

8. Determine whether or not the series converges $$\sum_{n=1}^{\infty}\frac{n^2}{n!}$$

   • Converges absolutely
   • Diverges
   • Converges conditionally
   • Oscillates

9. Determine whether or not the series converges $$\sum_{n=1}^{\infty}\sqrt{\frac{5n+2}{n^6+1}}$$

   • Converges by comparison test
   • Diverges by p-series
   • Converges conditionally
   • Diverges by nth-term test

10. Determine whether or not the series converges $$\sum_{n=1}^{\infty}\frac{4^n+2}{3^n}$$

    • Converges absolutely
    • Diverges
    • Converges conditionally
    • Alternating convergence