设Un=(x-1)^n/5^nUn+1=(x-1)^(n+1)/5^(n+1)比值法lim n→∞ |Un+1/Un|=lim |(x-1)^(n+1)/5^(n+1)/(x-1)^n/5^n|=|x-1|/5<1可得收敛区间R=5收敛区间(-4,6)当x=-4或6时,Un=±1不等于0所以此时级数发散即收敛域为(-4,6)
令X-1=y,你懂的高中代元法,把y解出范围和半径后,+1就是答案,