Interval of Convergence

[lala_doda]

Find the interval of convergence for the power series:
infinity
Sigma (1/(3ⁿ))((x-1)ⁿ)
n=0
I got that the radius is 4 and since it is centered around 1 the interval should be (-3,5), am I right?

 

[pka]

Find the interval of convergence for the power series: infinity
Sigma (1/(3ⁿ))((x-1)ⁿ)
n=0
I got that the radius is 4 and since it is centered around 1 the interval should be (-3,5), am I right?

You best think again there.
Using the absolute root test we get \(\displaystyle \dfrac{|x-1|}{3}<1\) as the basic set of convergence.
Now you need to test endpoints.

 

[lala_doda]

You best think again there.
Using the absolute root test we get \(\displaystyle \dfrac{|x-1|}{3}<1\) as the basic set of convergence.
Now you need to test endpoints.

oh okay, so it would be (-2,4), correct?

 

[pka]

Yes, that is correct. The radius of convergence is 3.