# Math Help - Ratio & root test question

1. ## Ratio & root test question

Is it true that if a series converges according to the ratio/root test, then the series converges to zero?

2. In general, no. Consider the series

$1=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\cdots$

where both the ratio $\frac{a_{k+1}}{a_k}$ and the root $(a_k)^{1/k}$ converge to $1/2$ as $k\rightarrow \infty$.