Given the series $$\sum_{n=0}^{\infty}(-1)^nx^{2^n}$$ determine the radius of convergence, and what can we say when $x=R$ and $-R$?
Is it a power series? Power series should have the form of $$\sum_{n=0}^{\infty}a_nx^n$$ but the given series does not match this form. If not a power series, why can we say about its radius of convergence?
By the ratio test, I get that this series converges when $|x|<1$, diverges when $|x|>1$, so $R=1$, is that right?
When $x=1$ or $-1$, series both becomes $$\sum_{n=0}^{\infty}(-1)^n,$$ then obviously, series diverges. Right?