Chapter Ten: Sequences and Series

Question 1

for what values of r does this geometric series converge? for what values does it diverge?

Answer 1

a geometric series converges for the values 0 < |r| < 1. a geometric series diverges for the values |r| ≥ 1

Question 2

for what values of p does this p-series converge? for what values does it diverge?

Answer 2

a p-series converges when p > 1, and diverges when p ≤1

Question 3

what is the sum of the geometric series?

Answer 3

a ÷ (1 - r)

Question 4

what is the sum of a telescoping series?

Answer 4