Solution
= Solution
For a series with eventually nonzero terms $a_n$, suppose $r=\lim_{n\to\infty}|a_{n+1}/a_n|$ exists. The <ratio test> says that $r<1$ implies <absolute convergence>, while $r>1$ implies divergence because the terms fail to tend to zero. At $r=1$ the test is \b[inconclusive].