Question

此高数题怎么求？

麻烦写纸上回复我 谢谢

Answer 1

收敛半径 R = lim<n→∞>a<n>/a<n+1>

= lim<n→∞>(n+1)4^(n+1)/(n4^n) = 4,
x = 4 时,级数变为 ∑<n=1,∞> 1/n 发散;
x = -4 时,级数变为 ∑<n=1,∞> (-1)^n/n 收敛.
则级数收敛域是 x∈[-4, 4)

Answer 2

consider
1/(1-u) = 1+u+u^2+...+
∫du/(1-u) =u+(1/2)u^2+(1/3)u^3+.....
u+(1/2)u^2+(1/3)u^3+.....=-ln|1-u|
u=x/4

∑(n:1->无穷) x^n/(n.4^n)
=-ln|1- x/4|
an= x^n/(n.4^n)
a(n+1)/an = (x/4)[ n/(n+1) ]
收敛半径
-4<x< 4