Calculus BC · Unit 10 · Paper 3

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 3” 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

Term-by-term differentiation and integration

Taylor series

Maclaurin series to know

nth term test for divergence

Absolute vs conditional convergence

Root test

Direct comparison test

Geometric series

Partial sums

Common series to recognize instantly

Taylor polynomial vs Taylor series

Interval of convergence endpoints

Short answer 1. Define or explain: p-series

3 pts

Short answer 2. Define or explain: Telescoping series

3 pts

Short answer 3. Define or explain: Power series centered at a

3 pts

Short answer 4. Define or explain: Choosing a convergence test

3 pts

Free response

9 pts

Consider the power series Σₙ₌₁^∞ (x − 2)ⁿ/(n·3ⁿ), and separately the Maclaurin series for cos x.

Find the radius of convergence of the power series.

Find the interval of convergence, testing both endpoints explicitly.

Use the first three nonzero terms of the Maclaurin series for cos x to approximate cos(0.2), and bound the error of that approximation.