Root test Quiz 1

Question 1

For which of the following series, the root test cannot be used?

Accepted Answer

$$\dfrac{b}{1}+\dfrac{b}{{{a}^{2}}}+\dfrac{b}{{{a}^{3}}}+...........\left( a > 0,b > 0 \right)$$

Answer

$$\dfrac{b}{1}+\dfrac{b}{{{a}^{2}}}+\dfrac{b}{{{a}^{3}}}+...........\left( a < 0,b > 0 \right)$$

Answer

Both of these

Answer

None of these

Question 2

The series $$\dfrac{b}{1}+\dfrac{b}{{{a}^{2}}}+\dfrac{b}{{{a}^{3}}}+...........$$  where $$a$$ and $$b$$ are greater than $$0$$.

Accepted Answer

Converge

Answer

Diverge

Answer

May converge or diverge

Answer

None of these

Question 3

The series $$\sum\limits_{n=1}^{\infty }{{{\left( 1+\dfrac{27}{n} \right)}^{n}}}$$

Accepted Answer

May converge or diverge

Answer

Converge

Answer

Diverge

Answer

None of these

Question 4

The series $$\sum\limits_{n=1}^{\infty }{\dfrac{{{n}^{n}}}{{{64}^{3n-1}}}}$$

Accepted Answer

Diverge

Answer

Converge

Answer

May converge or diverge

Answer

None of these

Question 5

The series $$\sum\limits_{n=1}^{\infty }{{{\left( \dfrac{27{{n}^{4}}+78}{28{{n}^{4}}-47{{n}^{3}}} \right)}^{n}}}$$

Accepted Answer

May converge or diverge

Answer

Converge

Answer

Diverge

Answer

None of these