(6)收敛, lim _(narrow infty )dfrac ({2)^n-1}({3)^n}=0.-|||-(7) n-dfrac {1)(n)} 发散.-|||-(8) [ {(-1))^n+1] dfrac (n+1)(n)} 发散.-|||-1.下列各题中,哪些数列收敛,哪些数列发散?对收敛数列,通过观察(xn)的变化-|||-趋势,写出它们的极限:-|||-(1) dfrac {1)({2)^n}} ;-|||-(2) {(-1))^ndfrac (1)(n)} ;-|||-(3) 2+dfrac {1)({n)^2}} ;-|||-(4)(n-11-|||-(5) { n{(-1))^n} ;-|||-(6)[2^n-1]-|||-(7) n-dfrac {1)(n)} ;-|||-(8) [ {(-1))^n+1] dfrac (n+1)(n)} -|||-解 (1)收敛, lim _(narrow infty )dfrac (1)({2)^n}=0.-|||-(2)收敛, lim _(narrow infty )((-1))^ndfrac (1)(n)=0.-|||-(3)收敛, lim _(narrow infty )(2+dfrac (1)({n)^2})=2.-|||-(4)收敛, lim _(narrow infty )dfrac (n-1)(n+1)=1.-|||-(e)(1)m