(6)设 _(n)=dfrac (3)(2)(int )_(0)^dfrac (n{n+1)}(x)^n-1sqrt (1+{x)^n}dx, 则极限limnan等于 ()-|||-(A) ((1+e))^dfrac (3{2)}+1 (B) ((1+{e)^-1)}^dfrac (3{2)}-1-|||-(C) ((1+{e)^-1)}^dfrac (3{2)}+1 (D) ((1+e))^dfrac (3{2)}-1

7.设-|||-._(1)=2 , _(n+1)=dfrac (1)(2)((x)_(n)+dfrac (2)({x)_(n)}) , n=1 ,2,3,...

+dfrac ({x)_(n+1)}({x)_(n)})

(B) dfrac (1)(n+1)sum _(i=1)^n(({X)_(i)-overline (X))}^2 .-|||-(C) dfrac (1)(n)s

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

dfrac (1)(n-1)sum _(i=1)^n(({X)_(i)-overline (X))}^2 .-|||-n-|||-C. sqrt (dfrac

6.设x_(1)=sqrt(6),x_(n+1)=sqrt(6+x_(n))(n=1,2,...),证明数列x_{n)}收敛，并求出极限值.6.设$x_{1}=

,(x)_(n),(x)_(n+1) 是来自N(μ,σ^2)的样本, overrightarrow ({x)_(n)}=dfrac (1)(n)sum _(i=

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

,(X)_(n+1))(ngt 1) 取自总体 sim N(mu ,(sigma )^2) . overline (X)=dfrac (1)(n)sum _(i

_(n)=dfrac (1)(2)((x)_(n-1)+dfrac ({a)^2}({x)_(n-1)}) n=1,2,···, 证明数列(xn)极限存在,并求