Direct comparison test Quiz 1

Question 1

What is $$5$$ times of  $$\sum\limits_{n=0}^{\infty }{\dfrac{2}{{{6}^{n}}}}$$

Accepted Answer

12

Answer

10

Answer

5

Answer

14

Question 2

Which series will be    $$\sum\limits_{n=0}^{\infty }{{{\left( -1 \right)}^{2n}}\dfrac{3}{{{2}^{n}}}}$$   compared to so that the series is convergent.

Accepted Answer

Geometric Series

Answer

Harmonic Series

Answer

Arithmetic Series

Answer

Fibonacci Series

Question 3

What is the nature of  $$\sum\limits_{n=0}^{\infty }{{{\left( -1 \right)}^{2n}}{{2}^{n+1}}}\dfrac{5}{{{2}^{n+1}}}$$

Accepted Answer

Diverges

Answer

$$\infty $$

Answer

$$-\infty $$

Answer

Converges

Question 4

Using Direct Comparison Test, Determine the nature of the series  $$\sum\limits_{n=1}^{\infty }{\dfrac{n}{n-{{\sin }^{2}}n}}$$

Accepted Answer

Diverges

Answer

$$\infty $$

Answer

$$-\infty $$

Answer

Converges

Question 5

Which of the following is an example of a diverging series?

Accepted Answer

$$\sum\limits_{n=0}^{\infty }{\dfrac{{{n}^{2}}+n+1}{n+1}}$$

Answer

$$\sum\limits_{n=0}^{\infty }{\dfrac{{{e}^{-n}}}{2{{n}^{2}}+4}}$$

Answer

$$\sum\limits_{n=0}^{\infty }{\dfrac{{{n}^{2}}+4}{{{e}^{n}}}}$$

Answer

$$\sum\limits_{n=1}^{\infty }{\dfrac{2n}{\left( 3n+1 \right)}{{n}^{2}}}$$