Ok

I will go in depth with this,

We know (hopefully) that

We also know

So now making a substitution we can see that

So now we know that integrating/differentiating a power series only changes the endpoint behavior

So we know that since

converges

So now we must check the endpoints.

At we have

Which diverges by the Alternating series test.

Since

Now we need to check at

We have

Which diverges by the integral test

So we have that

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Now for your second question we can see the by direct substitution into either the log or the equation, or seeing that

This implies that

is found by

Now once again we must check the endpoints,

so at

We have

Which as I showed earlier is divergent by the integral test.

But at

We have

Which as was shown earlier is convergent by the alternating series test.

Hope this helps.