Find intervals of convergence

I have a problem where the interval of convrsion is (0,2]

However, for the end points plugging the x=0, and x=2 back in is where i am having prolems.

I cannot figure it out what to do after i plug the x in. Can you someone help?

I will attempt to solve this problem using the ratio

I will attempt to properly cancel out.

then i get for an answer

so i plug x = 2 in to the original equation

Which is

From there i dont know what to do!

Can anyhelp me finish this and do the x = 0 also?

Thank you

Re: Find intervals of convergence

Quote:

Originally Posted by

**icelated** I have a problem where the interval of convrsion is (0,2]

However, for the end points plugging the x=0, and x=2 back in is where i am having prolems.

I cannot figure it out what to do after i plug the x in. Can you someone help?

I will attempt to solve this problem using the ratio

I will attempt to properly cancel out.

then i get for an answer

so i plug x = 2 in to the original equation

Which is

From there i dont know what to do!

Can anyhelp me finish this and do the x = 0 also?

Thank you

To show the series is divergent when , substitute into your series

This is the Harmonic Series, which is well known to be (and very easy to show that it is) divergent.

Re: Find intervals of convergence