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Cogito

AP Calculus BC · Chapter 3 · Lesson 2

Practice Worksheet

Geometric and Telescoping Series

Two series whose sums can be found exactly.

12 problems · about 21 minutes · LIM-7.A

NameDate

Figure — use these to answer the problems

Set the base below 1 and watch the terms shrink toward zero. That shrinking is what makes the sum finite.
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y = 1 · 0.5^x + 0
a, first term1
r, common ratio0.5
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. First term 10, ratio 0.5. What is the infinite sum?

    Answer

  2. What is the method for a telescoping series?

    • Find a closed form for the partial sum, then take its limit.
    • Find the common ratio.

  3. First term 4, ratio 0.5. Infinite sum?

    Answer

  4. First term 1, ratio 0.8. Infinite sum?

    Answer

  5. First term 3, ratio 0.25. Infinite sum?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. Ratio 1. Does the series converge? 1 yes, 0 no.

    Answer

  2. Ratio −0.5. Does it converge? 1 yes, 0 no.

    Answer

  3. First term 20, ratio 0.5. Infinite sum?

    Answer

Stretch Yourself

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

4 problems

  1. Which ratios give a convergent geometric series?

    • r = 0.3
    • r = negative 0.5
    • r = 1
    • r = 1.5
    • Tick every box that applies.

  2. First term 6, ratio 0.5. Infinite sum?

    Answer

  3. The Sum

    First term 8, ratio 0.5. What is the infinite sum?

    Answer

  4. The Divergent One

    Ratio 2. Does the series converge? 1 yes, 0 no.

    Answer