Understanding the Divergence Test and Infinite Series

The video tutorial explains the divergence test, also known as the nth term divergence test, which is used to determine if an infinite series diverges. It highlights that if the limit of the nth term as n approaches infinity is not zero, the series diverges. However, if the limit is zero, the test cannot conclude convergence or divergence. Two examples are provided: one with a series involving 11/13, which might converge or diverge, and another with 8/7, which diverges. The video also touches on infinite geometric series and uses graphing calculators to verify limits.

What does the divergence test conclude if the limit of the terms of a series is not zero?

• The series is finite.

• The series might converge or diverge.

• The series diverges.

• The series converges.

When applying the divergence test to the series with terms 11/13^n, what is the result of the limit?

• The limit is infinite.

• The limit is zero.

• The limit is less than zero.

• The limit is greater than one.

What can be concluded about the series with terms 11/13^n using the divergence test?

• The series converges.

• The series diverges.

• The series might converge or diverge.

• The series is finite.

In the graphical representation of the series 11/13^n, what do the terms approach as n increases?

• A constant value

• Negative infinity

• Zero

• Infinity

For the series with terms 8/7^n, what happens to the terms as n increases?

• They approach zero.

• They oscillate.

• They remain constant.

• They approach infinity.

What does the divergence test conclude for the series with terms 8/7^n?

• The series converges.

• The series diverges.

• The series might converge or diverge.

• The series is finite.

What is the base of the terms in the series 8/7^n?

• Greater than one

• Equal to one

• Less than one

• Negative

What is the significance of the base being greater than one in the series 8/7^n?

• The series is finite.

• The series oscillates.

• The series diverges.

• The series converges.

In the graphical representation of the series 8/7^n, what do the terms do as n increases?

• They decrease to negative infinity.

• They grow larger and approach infinity.

• They approach zero.

• They remain constant.

What type of series is both 11/13^n and 8/7^n considered to be?

• Arithmetic series

• Geometric series

• Harmonic series

• Fibonacci series