利用极限存在准则证明:-|||-(1) lim _(narrow infty )sqrt (1+dfrac {1)(n)}=1;-|||-(2) lim _(narrow infty )n(dfrac (1)({n)^2+pi }+dfrac (1)({n)^2+2pi }+... +dfrac (1)({n)^2+npi })=1;-|||-(3)数列 sqrt (2),sqrt (2+sqrt {2)},sqrt (2+sqrt {2+sqrt {2)}} 的极限存在;-|||-(4) lim _(xarrow 0)sqrt [n](1+x)=1;-|||-(5) lim _(xarrow {0)^+}x[ dfrac (1)(x)] =1.