高二数列的极限3

lim[n(1-1/3)(1-1/4)(1-1/5)....(1-1/(n+2))]=
=lim[n(2/3)(3/4)(4/5)...((n+1)/(n+2))]=
=lim2n/(n+2)=
=lim2/(1+2/n)=
=2.

n*2/3*3/4*4/5....n/(n+1)*(n+1)/(n+2)=n/(n+2)
*代表乘号

最后就是求lim(n/n+1),把每一项通分,之后就会看出有可约分的,结果是2