We know from Section 8.3 that the geometric series ar k (a 0) converges if 0

Question:

We know from Section 8.3 that the geometric series ∑ar^k (a ≠ 0) converges if 0 < r < 1 and diverges if r > 1. Prove these facts using the Integral Test, the Ratio Test, and the Root Test. Now consider all values of r. What can be determined about the geometric series using the Divergence Test?

Fantastic news! We've Found the answer you've been seeking!