A question about AP calculus BC

Question

In finding the interval of convergence for a geometric series, is an endpoint check necessary?

Answer 1

Hello Connie! No, you do not need an endpoint check for geometric series.

This is because the geometric series guarentees that if the radius of convergence is R, then the radius of convergence MUST be |R| < 1 ( |R| = 1 DOES NOT COUNT). Because of this, the interval of convergence for geometric series must also not need endpoint.

Side Note: For your informatuon, make sure that you DO use endpoint check for ratio tests because the ratio tests do not guarentee convergence at the endpoints.

I hope this helped! Let me know if additional explanation is needed. And good luck on your AP Calculus BC exam (I'm actually taking it this year too :) )!