Calculus BC · Unit 10 · Paper 1

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 1” 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

Taylor polynomial vs Taylor series

Building new series from known ones

Taylor series

Root test

nth term test for divergence

Choosing a convergence test

Taylor series centered elsewhere

Alternating series error bound in practice

Integral test

Series for a definite integral

Radius and interval of convergence

p-series

Short answer 1. Define or explain: Alternating series test

3 pts

Short answer 2. Define or explain: Term-by-term differentiation and integration

3 pts

Short answer 3. Define or explain: Geometric series

3 pts

Short answer 4. Define or explain: Alternating series error bound

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.