Root and Ratio Tests Quiz

Aria, Isla, and Zoe are having a friendly competition to see who can determine the convergence or divergence of a series. Which test should they use?

• series test

• convergent test

• convergence test

• divergence test

Olivia, Mia, and Luna are studying for their math exam. They come across a question about the root test. Can you help them figure out the condition for convergence in the root test?

• The limit of the absolute value of the nth root of the terms of the series must be greater than 1.

• The limit of the absolute value of the nth root of the terms of the series must be equal to 1.

• The limit of the absolute value of the nth root of the terms of the series must be greater than or equal to 1.

• The limit of the absolute value of the nth root of the terms of the series must be less than 1.

Liam, Isla, and Noah are studying for their math test. They come across a tricky concept. Can you help them understand? What is the condition for divergence in the root test?

• The limit of the absolute value of the nth root of a_n as n approaches infinity does not exist.

• The limit of the absolute value of the nth root of a_n as n approaches infinity is less than 1.

• The limit of the absolute value of the nth root of a_n as n approaches infinity is equal to 1.

• The limit of the absolute value of the nth root of a_n as n approaches infinity is greater than 1.

Luna, Samuel, and Elijah are studying for their math test. They come across a tricky concept about series and sequences. They want to know, what is the condition for convergence in the ratio test?

• Luna suggests: The limit of the absolute value of the ratio of consecutive terms in the series must be greater than 1.

• Samuel thinks: The limit of the absolute value of the ratio of consecutive terms in the series must be equal to 1.

• Elijah believes: The limit of the absolute value of the ratio of consecutive terms in the series must be greater than or equal to 1.

• Or, could it be that the limit of the absolute value of the ratio of consecutive terms in the series must be less than 1?

Olivia, Aria, and Grace are studying for their math test. They come across a tricky concept about the ratio test in series. Can you help them understand? What is the condition for divergence in the ratio test?

• The limit of the absolute value of the ratio of consecutive terms in a series is greater than 1.

• The limit of the absolute value of the ratio of consecutive terms in a series is not defined.

• The limit of the absolute value of the ratio of consecutive terms in a series is equal to 1.

• The limit of the absolute value of the ratio of consecutive terms in a series is less than 1.

Maya, Evelyn, and Zoe are having a friendly competition to see who can remember the formula for the root test. Can you help them out?

• Is it the limit as n approaches zero of the absolute value of the nth root of the absolute value of the terms in the series?

• Or is it the sum of the absolute value of the terms in the series?

• Could it be the limit as n approaches infinity of the absolute value of the nth root of the absolute value of the terms in the series?

• Or is it the product of the absolute value of the terms in the series?

Elijah, Nora, and Zoe are having a friendly competition to see who can remember their math formulas the best. They've come to the formula for the ratio test. Can you help them out?

• L = lim(n->∞) |(a(n+1)/a(n))|^n

• L = lim(n->∞) |(a(n+1)/a(n))|

• L = lim(n->∞) |(a(n+1)/a(n))| + 1

• L = lim(n->∞) |(a(n+1)/a(n))| - 1

Arjun, Scarlett, and Harper are on a quest to find the magical 'Root Test'. Can you help them understand its application?

• Is it used by Arjun to find the derivative of a function during their quest?

• Does Scarlett use it to find the limit of a sequence on their journey?

• Is it used by Harper to find the sum of a series in their adventure?

• Or, is the application of the 'Root Test' to determine the convergence or divergence of a series, helping them on their quest?

Ethan, Maya, and Jackson are discussing the applications of the ratio test in their math class. What is the primary application of the ratio test that they should focus on?

• Finding the average of an infinite series.

• Determining the convergence or divergence of an infinite series.

• Determining the limit of an infinite series.

• Finding the sum of an infinite series.

Jackson, Mia, and Lily are trying to determine the convergence or divergence of the series: ∑(n=1 to ∞) (1/2)^n. Can you help them figure it out?

• Remains constant

• Oscillates

• Diverges

• Converges