4.求下列极限:-|||-(1) lim _(narrow infty )(dfrac (1)(1cdot 2)+dfrac (1)(2cdot 3)+... +dfrac (1)(n(n+1)) =-|||-(3) lim _(narrow infty )(dfrac (1)(2)+dfrac (3)({2)^2}+... +dfrac (2n-1)({2)^n}) ;-|||-(5) lim _(narrow infty )(dfrac (1)({n)^2}+dfrac (1)({(n+1))^2}+... +dfrac (1)({(2n))^2}) ;-|||-(2) lim _(narrow infty )(sqrt (2)sqrt [n](2)sqrt (2)... sqrt [2](2)) =-|||-(4) lim _(narrow infty )sqrt [n](1-dfrac {1)(n)} =-|||-(6) lim _(narrow infty )(dfrac (1)(sqrt {{n)^2+1}}+dfrac (1)(sqrt {{n)^2+2}}+... +dfrac (1)(sqrt {{n)^2+n}})-|||-人旦发散数列.证明 {a)_(n)pm (b)_(n)| 是发数数列