因为级数∞n＝1(−1)nlnn+1n为交错级数，un＝lnn+1n．由于，un+1−un＝lnn+2n+1−lnn+1n＝ln(n+2)n(n+1)2＝lnn2+2nn2+2n+1＜0所以数列{un}单调减少而且limn→∞un＝limn→∞lnn+1n＝0．因此由Leibniz判别法知，级数...