?11、 级数求和：

n?1?n?1??z?1?n22nn??3n?1??z?1?n?1??n?n??1?n?!zn2?x?1????k?02k?1?x?1?2k?1

?x?0?>> syms z n

>> symsum((z-1)^n/(n^2*2^n),n,1,inf) ans =

(1/2*z-1/2)*hypergeom([1, 1, 1],[2, 2],1/2*z-1/2)

>> syms z n

>> symsum((3*n+1)*(z-1)^n,n,1,inf) ans =

(4*z-4)*(-1/(z-2)+3/4/(z-2)^2*(z-1))

>> syms z n

>> symsum(n*(-1)^(n+1)*z^n,n,1,inf) ans = z/(z+1)^2

>> syms x positive >> syms k

>> simple(symsum(2/(2*k+1)*((x-1)/(x+1))^(2*k+1),k,0,inf)) ans =

log(-(1+((x^2-2*x+1)/(x^2+2*x+1))^(1/2))/(-1+((x^2-2*x+1)/(x^2+2*x+1))^(1/2)))