lim(1-1/2n).(1+1/2+1/4+.+1/2^n)

问题描述:

lim(1-1/2n).(1+1/2+1/4+.+1/2^n)

lim(1-1/2n).(1+1/2+1/4+.+1/2^n)
lim(1+1/2+1/4+…….+1/2^n)(1-1/2n)
lim[(1-1/2^n+1)/(1-1/2)][1-1/2n]
lim[2-1/2^n][1-1/2n]
=lim[2-1/2^n]lim[1-1/2n]
=2*1
=2