AP Calculus BC Unit 10 — Infinite Sequences and Series Practice Test

If the following infinite geometric series converges, find its sum. 1−3+3² −3 ³ …

True or false? According to the n^th term test, the series converges.

When applying the integral test, we get a limit that determines whether the series converges or diverges. What is this limit?

Which of the following series diverges? Choose all answers that apply.

We know that

Considering this fact, what does the direct comparison test say about

What series should we use in the limit comparison test in order to determine whether S converges?

Which series converges?   

Which of the following series cannot be shown to converge using the limit comparison test with the series shown.

Given the limit shown, what can you conclude about the infinite series ∑a _n ?   

What is the approximate of sin(1) using the fifth-degree Taylor polynomial centered at x=0 for sin x ?

Estimating cos (1.3 π ) using a Taylor polynomial about x=1.5 π , what is the least degree of the polynomial that assures an error smaller than 0.001 ?

What is the interval of convergence for the power series given?

What are the first three non-zero terms of the Maclaurin series for the function f ( x)=xcos ( x ) ?

We know that

Using this fact, find the function that corresponds to the following series.