判断无穷级数∑n=1∞(n+1)/3n的敛散性．
∵limn→∞un+1/un=limn→∞[(n+2)/3n+1]/ [(n+1)/3n]=limn→∞(n+2)/[3(n+1)]=1/3﹤1 ∴由达朗贝尔判别法得，原级数收敛．
判断无穷级数∑n=1∞(n+1)/3n的敛散性．
∵limn→∞un+1/un=limn→∞[(n+2)/3n+1]/ [(n+1)/3n]=limn→∞(n+2)/[3(n+1)]=1/3﹤1 ∴由达朗贝尔判别法得，原级数收敛．
