Determine whether the seriesnbspsumn0infin epin converges

Question

1. Determine whether the series ∑_n=0^∞ (e/Π)ⁿ converges or diverges. If it converges. find its sum.

Select the correct choice below and, if necessary. fill in the answer box within your choice.

A. The series diverges because it is a geometric series with |r| ≥ 1.

B. The series converges because lim_k→∞ ∑_n=0^k(e/Π)ⁿ fails to exist.

C. The series converges because it is a geometric series with |r| < 1 The sum of the series is __.

D. The series converges because lim_n→∞(e/Π)ⁿ = 0. The sum of the series is __.

E. The series diverges because lim_n→∞ (e/Π)ⁿ ≠ 0 or fails to exist.