Question

幂级数(x^n)/(2*4*.(2n))的收敛域

Answer 1

an=(x^n)/(2*4*.(2n))=x^n/[(2^n)(n!)]

因为lima(n+1)/an=[x^(n+1)/[(2^(n+1))((n+1)!)]]/[x^n/[(2^n)(n!)]]

=lim{x/[2(n+1)]}=0

所以收敛域为R