Find the radius r of convergence for the series ∞ 4n x2n 5n 1 n

Determine whether the geometric series. ∞. ∑ n=1 en. 3n-1 is convergent or divergent. If it isconvergent, find its sum. Answer: I can re-write the terms as en. 3n-1 ... (n n + 1.) = lim n→∞ sn = limn→∞. (-ln (n + 1)) = - ∞, so the given series diverges. 48. Find the values of x for which the series. ∞. ∑n=1. (x - 4) n converges.