Question

lim(2nan)=1,且liman存在,则lim[(1-n)an]=

Answer 1

使用极限的四则运算法则.

∵lim{n → ∞} 2n·a[n] = 1,

∴lim{n → ∞} n·a[n] = 1/2,

又∵lim{n → ∞} 1/n = 0,

∴lim{n → ∞} a[n] = (lim{n → ∞} 1/n)·(lim{n → ∞} n·a[n]) = 0,

∴lim{n → ∞} (1-n)a[n] = lim{n → ∞} a[n] - lim{n → ∞} n·a[n] = -1/2.