# Math Help - Match each of the following with the correct statement #2

1. ## Match each of the following with the correct statement #2

Match each of the following with the correct statement.
A. The series is absolutely convergent.
C. The series converges, but is not absolutely convergent.
D. The series diverges.

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2. Originally Posted by ewkimchi
Match each of the following with the correct statement.
A. The series is absolutely convergent.
C. The series converges, but is not absolutely convergent.
D. The series diverges.

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The ratio test works well to show if the series are absolutely convergent...

If $\lim_{n \to \infty}\left|\frac{t_{n + 1}}{t_n}\right| < 1$ then the series is absolutely convergent, if $\lim_{n \to \infty}\left|\frac{t_{n + 1}}{t_n}\right| > 1$ the series is divergent, and if $\lim_{n \to \infty}\left|\frac{t_{n + 1}}{t_n}\right| = 1$, the test is inconclusive and you'll need to use a different test.