Calc Exam 3

True or False?

True

True or False?

True

True or False?

False

True or False?

False

If the image is true, the series is ____ convergent.

absolutely

If the image is true, the series is ____ convergent.

conditionally

What is this theorem called?

Absolute Convergence implies convergence

If a series converges absolutely, then the series converges. If a series converges, does it converge absolutely?

No

What is an example of a series that converges, but not absolutely?

The alternating series

What is this theorem called?

The Ratio Test

Per the ratio test, if 0≤p<1, then the series is

absolutely convergent

Per the ratio test, if p>1 or p= positive infinity, then the series

diverges

Per the ratio test, if p=1, then the ratio test is

inconclusive

What is this theorem called?

The Root Test

Per the root test, if 0≤p<1, then the series is

absolutely convergent

Per the root test, if p>1 or p= positive infinity, then the series

diverges

Per the root test, if p=1, then the ratio test is

inconclusive

If a factorial is present in the equation, should you use the root or ratio test?

Ratio

If both denominator and numerator are raised to a power, should you use the root or ratio test?

Root

What kind of series is this?

power series

If x=a, the power series

converges

If x does not equal a, apply the ___ test.

ratio

If there exists R>0 such that the series converges for |x-a|<R, and diverges for |x-a|> R, then R is the __________.

radius of convergence

If the series converges, only at x=a, R=_.

0

If the series converges for all x real numbers, R= ___

positive infinity

What do you use to find the radius and interval of convergence?

ratio test

When can we represent a function by a power series?

When it is continuous and does not only converge at the center