A. $\int_{0}^{1} \sqrt{x} \, dx$
B. $\int_{0}^{1} \sqrt{1 + x} \, dx$
C. $\int_{1}^{2} \sqrt{x} \, dx$
D. $\int_{1}^{2} \sqrt{1 + x} \, dx$
59 lim_(n to infty ) sum_(i=1)^n (n)/(n^2)+i^(2+1)=____59 $\lim_{n \to \infty }
若 lim_(n to infty) u_n = 0，则级数 sum_(n=1)^infty u_n（）A. 一定收敛B. 一定发散C. 绝对收敛D. 可能收敛
判别下列级数的绝对收敛性与收敛性：(1) sum_(n=1)^infty (i^n)/(n); (2) sum_(n=2)^infty (i^n)/(ln n
若lim_(n to infty) b_n = +infty, 则级数sum_(n=1)^infty ((1)/(b_n) - (1)/(b_(n+1)) )的
2、设级数sum_(n=1)^inftya_(n)收敛，lim_(ntoinfty)na_(n)=a.证明：sum_(n=1)^inftyn(a_(n)-a_(
13.设 sum _(i=1)^infty (a)_(n)=1, 则 sum _(n=1)^infty ((a)_(n)-2(a)_(n+1))= __
,则 a= ())0,&({lim)} _(x arrow infty)|(1)/(n) {{sum)}_(i=1)^n X_i-a|0,\\&{{\l
【例】求极限lim_(ntoinfty)((1)/(n+1)+(1)/(n+sqrt(2))+...+(1)/(n+sqrt(n)))。【例】求极限$\lim_
dfrac (1)(n-1)sum _(i=1)^n(({X)_(i)-overline (X))}^2 .-|||-n-|||-C. sqrt (dfrac
根据数列极限的定义证明：(1) lim_(n to infty) (1)/(n^2) = 0;(2) lim_(n to infty) (3n+1)/(2n+1