Power Series | Power Series & Interval of Convergence: Example 2

The video tutorial explains how to determine the interval of convergence for a power series using the root test. It begins with an introduction to the series and discusses why the root test is preferred in this case. The tutorial then walks through the calculation of the limit, evaluates it, and concludes that the series converges for all values of x, resulting in an infinite radius of convergence. The video emphasizes that this is a straightforward case and highlights the significance of the result.

Which test is deemed most suitable for determining the interval of convergence in this series?

• Ratio test

• Root test

• Integral test

• Comparison test

What happens to the powers of n when applying the root test to the series?

• They double

• They become negative

• They remain unchanged

• They cancel out

What is the limit of 1/n as n approaches infinity?

• 1

• Infinity

• Undefined

• 0

Why does the series converge for all values of x?

• Because the limit is a function of x

• Because the limit is negative

• Because the limit is greater than 1

• Because the limit is zero, which is always less than 1

What is the radius of convergence for this power series?

• Finite

• Undefined

• Infinite

• Zero