设 ^2=sum _(n=0)^infty (a)_(n)cos nx,(-pi leqslant xleqslant pi ), 则 _(3)= __ 艹

判断级数sum _(n=1)^infty (2)^nsin dfrac (pi )({3)^n}的敛散性。判断级数的敛散性。

2.已知数列(xn),其中 -dfrac (pi )(2)leqslant (x)_(n)leqslant dfrac (pi )(2) ,则 ()-|||-(

5.当0≤x≤(pi)/(2)时，lim_(ntoinfty)sqrt[n](sin^nx+cos^nx)=____.5.当0≤x≤$\frac{\pi}{2}

设-|||-.f(x)= { sin x, 0leqslant xleqslant pi , 0, xlt 0或xgt pi f(t)dt 在 (-inf

设幂级数 sum _(n=0)^infty (a)_(n)(x)^n 的收敛半径为 (0lt Rlt +infty ), 则 sum _(n=0)^infty

设 M=int_(-(pi)/(2))^(pi)/(2) (sin x)/(1+x^2) cos^4 x dx，N=int_(-(pi)/(2))^(pi)/(

13.设 sum _(i=1)^infty (a)_(n)=1, 则 sum _(n=1)^infty ((a)_(n)-2(a)_(n+1))= __

20.[单选题] 设 =cos i ,则 ()-|||-A (A) lim _(narrow infty )(m)_(n)=0-|||-~z=0;-|||-B

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

5.已知 (x)=sum _(n=1)^infty ((-1))^n-1dfrac (1)((2n-1)!)((pi x))^2n-1 则 f(1)=()-||