Convergence and divergence Quiz 1

Question 1

Is the given series $$1-\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{4}+........$$ absolutely convergent?

Accepted Answer

No, conditionally convergent

Answer

Yes

Answer

No, divergent

Answer

None of the above

Question 2

Find the nature of the series  $$1+\dfrac{1}{{{2}^{2}}}+\dfrac{{{2}^{2}}}{{{3}^{3}}}+\dfrac{{{3}^{3}}}{{{4}^{4}}}+\dfrac{{{4}^{4}}}{{{5}^{5}}}+........$$.

Accepted Answer

Divergent

Answer

Convergent

Answer

Conditionally divergent

Answer

Oscillatory

Question 3

Is $${{a}_{n}}=\dfrac{1}{n}\sin \dfrac{n\pi }{2}$$ convergent?

Accepted Answer

Yes

Answer

No, conditionally divergent

Answer

No, absolutely divergent

Answer

No, oscillatory

Question 4

Find the nature of the series $${{\left( \dfrac{1}{3} \right)}^{2}}+{{\left( \dfrac{1 \cdot 2}{3 \cdot 5} \right)}^{2}}+{{\left( \dfrac{1 \cdot 2 \cdot 3}{3 \cdot 5 \cdot 7} \right)}^{2}}+.........$$

Accepted Answer

Convergent

Answer

Divergent

Answer

Conditionally divergent

Answer

Oscillatory

Question 5

Determine the nature of the series given by $${{\left( \dfrac{{{2}^{2}}}{{{1}^{2}}}-\dfrac{2}{1} \right)}^{-1}}+{{\left( \dfrac{{{3}^{3}}}{{{2}^{3}}}-\dfrac{3}{2} \right)}^{-2}}+{{\left( \dfrac{{{4}^{4}}}{{{3}^{4}}}-\dfrac{4}{3} \right)}^{-3}}+...$$

Accepted Answer

Convergent

Answer

Divergent

Answer

Oscillatory

Answer

Cannot be determined