(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

(3)收敛, lim _(narrow infty )(2+dfrac (1)({n)^2})=2 --|||-(4)收敛, lim _(narrow inft

2.按 -N 定义证明:-|||-(1) lim _(narrow infty )dfrac (n)(n+1)=1 ;-|||-(2) lim _(narrow

+(n)^3);-|||-(2) lim _(narrow infty )n[ dfrac (1)({(n+1))^2}+dfrac (1)({(n+2))^2

+dfrac (1)(n(n+1)) =-|||-(3) lim _(narrow infty )(dfrac (1)(2)+dfrac (3)({2)^2}+

根据数列极限定义证明：(1) lim _(narrow infty )dfrac (1)({n)^2}=0-|||-(2) lim _(narrow infty

(2) lim _(narrow infty )dfrac (3n+1)(2n+1)=dfrac (3)(2) ;

求极限lim _(narrow infty )dfrac ({2)^n+(3)^n+(7)^n}({5)^n+(8)^n}lim _(narrow infty

lim _(narrow infty )(dfrac (1)({n)^2+n+1}+dfrac (2)({n)^2+n+2}+... +dfrac (n)({n

lim _(narrow infty )dfrac ({2)^n+(3)^n}({2)^n+1+(3)^n+1}=________;________;

+dfrac (1)({2)^n})-|||-1/2^n);(12)-|||-(13) lim _(narrow infty )dfrac ((n+1)(n+2