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Cogito

AP Calculus BC · Chapter 4 · Lesson 1

Practice Worksheet

Choosing a Convergence Test

Which tool for which series.

11 problems · about 26 minutes · AP Calculus BC 10.3, 10.5, 10.8

NameDate

Figure — use these to answer the problems

The ratio test compares its limit against 1.
0123

1

The ratio limit1
Figure 1

Warm Up

Straightforward practice. Get the method working first.

4 problems

  1. Sum of 1/n^0.5. Converge? 1 for yes, 0 for no.

    Answer

  2. Sum of 1/n⁴. Converge? 1 for yes, 0 for no.

    Answer

  3. Geometric with r = 0.9. Converge? 1 for yes, 0 for no.

    Answer

  4. Geometric with r = 1.1. Converge? 1 for yes, 0 for no.

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. Ratio test limit is 0.4. Converge? 1 for yes, 0 for no.

    Answer

  2. Ratio test limit is exactly 1. Is the test decisive? 1 for yes, 0 for no.

    Answer

  3. Sort each series by whether it converges.

    Write each item under the heading it belongs to: Sum of 1/n² · Sum of 1/n · Geometric, r = 1/2 · Sum of n

    Converges

    Diverges

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

4 problems

  1. Terms approach 3, not 0. Converge? 1 for yes, 0 for no.

    Answer

  2. Match each series to the test that settles it most directly.

    Draw a line from each item on the left to its match on the right.

    • Terms approach 5
    • Sum of 1/n^1.5
    • Terms with factorials
    • nth term test
    • p-series
    • Ratio test

  3. A p-Series

    Sum of 1/n³. Does it converge? 1 for yes, 0 for no.

    Answer

  4. The Borderline

    Sum of 1/n. Does it converge? 1 for yes, 0 for no.

    Answer