Find radius of convergence and interval of convergence for the series

[emk]

x^n/(2n-1) is the series. It starts at 1 and goes to infinity.

I did the ratio test on it and got abs.(x)

So the radius of convergence=1, and then I plugged -1 and 1 into the original series and got that they both converged. But the answer is [-1,1). Why aren't they both hard brackets?

 

[STEMucator]

x^n/(2n-1) is the series. It starts at 1 and goes to infinity.

I did the ratio test on it and got abs.(x)

So the radius of convergence=1, and then I plugged -1 and 1 into the original series and got that they both converged. But the answer is [-1,1). Why aren't they both hard brackets?

Pay special attention to x=1. When you plug it into your series you get $\sum \frac{1}{2n-1}$.

You know that diverges...

Hint : Compare it to something you know diverges already.