1.limn^(3/2)sin(1/n)/根号(n+1)=1,级数收敛2.lim[(n+1)/2^n]^(1/n)=(1/2)lim[(n+1)]^(1/n)=1/2<1, 级数收敛3.lim[(n+1)^2*2^(n+1)/(n+2)!]/[n^2*2^n/(n+1)!]=lim2(1+1/n)^2/(n+2)=0<1，级数收敛
