(1) R = lima/a = lim n!/(n+1)! = lim1/(n+1) = 0;(2) R = lima/a = lim (n+1)2^(n+1)/(n2^n) = 2,x = 2 时级数变为 ∑1/n 发散，x = -2 时级数变为 ∑(-1)^n/n 收敛，收敛域 x∈ [-1, 1).(3) 隔项级数，R^2 = lima/a = lim (2n+1)/(2n-1) = 1,收敛半径 R = 1.x = 1 时级数变为 ∑1/(2n-1) > ∑1/(2n) = (1/2)∑1/n 发散，x = -1 时级数变为 ∑-1/(2n-1) 发散，收敛域 x∈ (-1, 1).(4) R = lima/a = lim√(n+1)/√n = 1,-1 < x - 5 < 1, 4 < x < 6,x = 4 时级数变为 ∑(-1)^n/√n 收敛，x = 6 时级数变为 ∑1/√n 发散，收敛域 x∈ [4, 6).
