Tests for Divergence & Convergence (College Board AP® Calculus BC): Exam Questions

State the necessary conditions for using the integral test to determine whether or not the series converges. Use the integral test to show that converges.

A function is defined in power series form by . Explain whether or not the series will converge for .

Given that is a convergent series, use the limit comparison test to show that converges absolutely.

Give a value of such that converges, but diverges. Give reasons why your value of is correct.

Consider the convergent series . Show that approximates the value of the series sum with error less than .

A function is given in power series form as . Determine whether the series for converges or diverges at . Give a reason for your answer.

Determine whether or not the series converges. Justify your answer.

Use the integral test to prove that the -series converges for and diverges for . Be sure to state the necessary conditions for using the integral test to determine convergence or divergence of these series.

Determine whether the series converges or diverges. State and confirm the conditions of the test used for determining convergence or divergence.

Determine whether the series converges absolutely, converges conditionally, or diverges. Justify your answer.