What if ratio test equals 1

Here is the limit. In order to do this limit we will need to eliminate the factorials. Do not mistake this for a geometric series.

In the previous example the absolute value bars were required to get the correct answer. Recall that the ratio test will not tell us anything about the convergence of these series. We will need to resort to another test for this series. The two conditions are met and so by the Alternating Series Test this series is convergent. Again, the ratio test tells us nothing here. We can however, quickly use the divergence test on this. In fact that probably should have been our first choice on this one anyway.

There is one more thing that we should note about the ratio test before we move onto the next section. We want to use root test here because we see a lot of powers of n. So let. Approximating functions with Taylor polynomials and error bounds. Back to Course Index. You can still navigate around the site and check out our free content, but some functionality, such as sign up, will not work.

If you do have javascript enabled there may have been a loading error; try refreshing your browser. Home Calculus Sequence and Series. Still Confused? Nope, got it. Play next lesson. Try reviewing these fundamentals first Introduction to infinite series Convergence and divergence of normal infinite series. That's the last lesson Go to next topic. Still don't get it? Review these basic concepts… Introduction to infinite series Convergence and divergence of normal infinite series Nope, I got it.

Play next lesson or Practice this topic. Play next lesson Practice this topic. Start now and get better math marks! Intro Lesson. Lesson: 1a. Lesson: 1b. Lesson: 1c. Lesson: 1d. Lesson: 2. Intro Learn Practice. Ratio Test Convergence tests are used to find the convergence of series or power series.

Then we say that: Formula 1: Ratio test. Equation 1: Convergence Ratio test pt. Equation 2: Divergence Ratio test pt.

Formula 2: Root test. Equation 3: Divergence Root test pt. Formula 3: Power Series. Formula 4: Interval of Convergence pt. Equation 4: Ratio test Interval of Convergence pt. Equation 5: Root test Interval of Convergence pt. Do better in math today Get Started Now. Introduction to sequences 2. Monotonic and bounded sequences 3. Introduction to infinite series 4. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields.

It only takes a minute to sign up. Connect and share knowledge within a single location that is structured and easy to search. The idea behind it, why it works is the geometric series which dominates or not the tested series.

I have no understanding and no intuition for that case. The reason this test is inconclusive is that even two series with exactly the same successive ratios can have different convergence properties when the limit of the successive ratios are 1. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group.

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