5.13 Ratio test

Ratio test

Lessons

Notes:
Note *Let an\sum a_n be a series. Then we say that

R=R=lim\limn →\infty an+1an\mid \frac{a_{n+1}}{a_n}\mid

Where:
1. If RR < 11, then the series is convergent (or absolutely convergent)
2. If RR > 11, then the series is divergent
3. If R=1R=1, then the series could either be divergent, or convergent

Basically if R=1R=1, then the ratio test fails and would require a different test to determine the convergence or divergence of the series.
  • 2.
    Convergence & Divergence of Ratio Test
    Use the Ratio Test to determine if the series converges or diverges. If the ratio test does not determine the convergence or divergence of the series, then resort to another test.
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Ratio test

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