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Cogito

AP Calculus BC · Chapter 3 · Lesson 1

Practice Worksheet

Sequences and Partial Sums

A list, and the running total of that list.

11 problems · about 24 minutes · AP Calculus BC 10.1, 10.2

NameDate

Figure — use these to answer the problems

Partial sums creep along the line, each one closer to the limit.
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1

A partial sum1
Figure 1

Warm Up

Straightforward practice. Get the method working first.

4 problems

  1. Geometric with a = 3, r = 1/2. What does it converge to?

    Answer

  2. 1 + 3 + 5. Third partial sum?

    Answer

  3. Geometric with a = 1, r = 1/3. What does it converge to? Give it as a decimal to two places.

    Answer

  4. Do the terms of the harmonic series go to zero? 1 for yes, 0 for no.

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. Does the harmonic series converge? 1 for yes, 0 for no.

    Answer

  2. Sort each object by what it is.

    Write each item under the heading it belongs to: 1, 2, 3, 4, … · 1 + 2 + 3 + 4 + … · The list of partial sums

    A sequence

    A series

  3. Geometric with a = 2, r = 1/2. Sum?

    Answer

Stretch Yourself

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

4 problems

  1. Geometric with r = 2. Does it converge? 1 for yes, 0 for no.

    Answer

  2. 5 + 5 + 5. Third partial sum?

    Answer

  3. Three Terms

    For 2 + 4 + 6, what is the third partial sum?

    Answer

  4. The Geometric Sum

    1 + 1/2 + 1/4 + … converges to what value?

    Answer