Does $\sum_{n=0}^{\infty}\frac{4^n}{4^{n+1}}$ Diverge Or Converge? I am told it diverge, however surely;
$$\frac{4^n}{4^{n+1}} = \frac{4^n}{4\cdot 4^n} = \frac{1}{4}$$

The series diverges, because
$$\lim_{n \to \infty} \frac{4^n}{4^{n+1}} =  \lim_{n \to \infty} \frac{1}{4} = \frac{1}{4}$$
and a series can only converge if the sequence that is summed up converges to $0$.
