企源知识库

判断无穷级数∑_n=1^∞(n+1)/3ⁿ的敛散性．
【正确答案】：∵lim_n→∞u_n+1/u_n=lim_n→∞[(n+2)/3ⁿ⁺¹]/ [(n+1)/3ⁿ]=lim_n→∞(n+2)/[3(n+1)]=1/3﹤1 ∴由达朗贝尔判别法得，原级数收敛．