+dfrac (sin n)({2)^n} ;-|||-(2) _(n)=1+dfrac (1)({2)^2}+dfrac (1)({3)^2}+... +dfrac (1)({n)^2}

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

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

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

_(n)=((-1))^n+1dfrac (1)(sqrt {n)}-|||-C. _(n)=sin dfrac (npi )(2)-|||-D. _(n)=d

+dfrac (1)({(2n-1))^2}(2n-1)x+... ] -|||-(B) dfrac (2)(pi )[ dfrac (1)({2)^2}sin

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

+dfrac (n)({n)^2+n+n})=dfrac (1)(2)证明：

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

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

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