4(1) lim|a| = lim1/n = 0|a| = 1/(n+1) < 1/n = |a| , 根据交错级数收敛性的判定定理,该级数收敛,但条件收敛。(2) ∑1/(2n-1) > ∑1/(2n) = (1/2)∑1/n后者发散,则原级数发散。(3) ∑|sinn/2^n| < ∑1/2^n = 1后者收敛,则原级数收敛,且绝对收敛。