计算下列数列的极限：
(1)limn→∞(2n3+n-1)/(3n3-n2+2)；
(2)limn→∞(2n+1)/(2n+3)；
(3)limn→∞[(2/3)n+(5/7)n+1+3]；
(4)limn→∞(1+2+…+n)/nn；
(5)limn→∞[(3n2+2)2/(1-4n2)]．
(1)limn→∞(2n3+n-1)/(3n3-n2+2)=limn→∞[(2+1/n2-1/n3)/(3-1/n+2/n3)]=2/3 (2)limn→∞(2n+1)/(2n+3)=limn→∞[(1+(1/2)n)/(1+3/2n)]=1 (3)limn→∞[(2/3)n+(5/7)n+1+3]=0+0+3=3 (4)limn→∞(1+2+…+n)/n2=limn→∞[(1+n)•n/2n2]=limn→∞[(n+1)/2n]=[(1+1/n)/2]=1/2 (5)limn→∞[(3n2+2)2/(1-4n2)]=limn→∞[(3+2/n2)/(-4+1/n2)]2=[-(3/4)2]=9/16
