Calculus BC · Unit 10 · Paper 2

Infinite Sequences & Series unit test

A test on this unit alone, marked as a percentage and a letter grade — for the test your class is actually sitting, rather than for May. Answer everything, then submit once: seeing the answer to question 3 before attempting question 4 makes the final percentage meaningless.

Paper 1 Paper 2 Paper 3

Each paper is built from this unit’s 30 terms and is the same for everyone, so a teacher can assign “Unit 10, Paper 2” and every student sits the identical test. Multiple choice is marked objectively; the written sections you mark yourself against the model answer and rubric.

Suggested time 36 min 33 points0/17 attempted

Choosing a convergence test

Sequence vs series

Alternating series error bound

Root test

nth term test for divergence

Lagrange error bound

Geometric series

Manipulating the geometric series

Telescoping series

Partial sums

Taylor polynomial vs Taylor series

Taylor series

Short answer 1. Define or explain: Common series to recognize instantly

3 pts

Short answer 2. Define or explain: Alternating series test

3 pts

Short answer 3. Define or explain: Maclaurin series to know

3 pts

Short answer 4. Define or explain: Ratio test

3 pts

Free response

9 pts

Let f(x) = ln(1 + x).

Write the first four nonzero terms and the general term of the Maclaurin series for f.

Determine the interval of convergence of that series, showing the analysis at both endpoints.

Use the first three nonzero terms to approximate ln(1.1), and bound the error.