Which of the following statements is true for the series the summation from n equals 0 to infinity of the nth power of the quotient of e and pi ?

Question

Which of the following statements is true for the series  ?

A	Converges to
B	Converges to
C	Converges to
D	Diverges

Answer 1

0 < r = e/π < 1. By formula of sum infinite geometric serie S_∞ = a₁/(1 - r);

∑₀^∞(e/π)ⁿ = 1/(1 - e/π) = π/(π - e).

Converges to π/(π - e). B. is right answer.