证明：级数sum _(n=1)^infty (sin dfrac (1)({n)^2})收敛。

A12.1.4 下列级数中,收敛的级数是 __-|||-(A) sum _(n=1)^infty =dfrac (-2)(n) (B) sum _(n=1)^i

(4)下列级数中,条件收敛的级数为 () .-|||-(A) sum _(n=1)^infty ((dfrac {1+3i)(2))}^n (B) sum _(

1.求下列幂级数的收敛域(或收敛圆):-|||-(1) sum _(n=1)^infty dfrac (1)({2)^n}(x)^2n-1;-|||-(2) s

) ,若级数 sum _(n=1)^infty (a)_(n),sum _(n=1)^infty (b)_(n) 收敛,则 sum _(n=1)^infty (

下列级数绝对收敛的是()A.sum _(n=1)^infty dfrac ({(-1))^n+1}(2n+1)B.sum _(n=1)^infty dfrac

设幂级数sum _(n=1)^infty (a)_(n)((x-2))^n在sum _(n=1)^infty (a)_(n)((x-2))^n处收敛，则此幂级数

1.用比较审敛法判别下列级数的敛散性.-|||-(1) sum _(n=1)^infty sin dfrac (pi )({n)^2}-|||-(2) sum

求级数sum _(n=1)^infty dfrac ({4)^n}(2+{n)^3}(x)^n的收敛区间?求级数的收敛区间?

1.求下列幂级数的收敛半径、收敛区间、收敛域.-|||-(1) sum _(n=1)^infty ((-1))^n-1dfrac ({x)^n}({n)^2}

4、求幂级数 sum _(n=1)^infty dfrac ({(-1))^n}(n)((x-1))^n 的收敛域.