微积分级数问题

2025-04-06 21:07:07
推荐回答(1个)
回答1:

5. 为缺项级数,记收敛半径为R,则
R^2 = lima/a
= lim(2n)![(n+1)!]^2 / {[2(n+1)]!(n!)^2}
= lim(n+1)^2 / [(2n+2)(2n+1)]
= lim(n+1) / [2(2n+1)] = 1/4,
收敛半径 R = 1/2
x = ±1/2 时,级数发散。收敛域是 (-1/2, 1/2)