Ratio test Quiz 1

Question 1

Find whether the series $$\sum\limits_{n=0}^{\infty }{\ln \left( 1+\dfrac{1}{{{n}^{2}}} \right)}$$ is:

Accepted Answer

convergent

Answer

divergent

Answer

neither convergent nor divergent

Answer

none of the above

Question 2

Find whether the series $$\sum\limits_{n=0}^{\infty }{\dfrac{\sin {{(n-1)}^{n-1}}}{n!}}$$ is:

Accepted Answer

divergent

Answer

convergent

Answer

oscillatory

Answer

none of the above

Question 3

Find whether the series $$\sum\limits_{n=0}^{\infty }{{{2}^{n-1}}{{(n-1)}^{n}}}$$ is:

Accepted Answer

divergent

Answer

convergent

Answer

neither convergent or divergent

Answer

none of the above

Question 4

Find whether the series $$\sum\limits_{n=0}^{\infty }{{{7}^{-n}}{{(n)}^{7}}}$$ is:

Accepted Answer

convergent

Answer

divergent

Answer

oscillatory

Answer

none of the above

Question 5

Find whether the series $$\sum\limits_{n=0}^{\infty }{\dfrac{{{	an }^{-1}}\sqrt{n-1}}{\sqrt{n-1}}}$$ is:

Accepted Answer

none of the above

Answer

convergent

Answer

divergent

Answer

oscillatory