(2-√x)^n=2^n+n√x*2^(n-1)+x*2^(n-2)*n(n-1)/2+…………
an=2^(n-2)*n(n-1)/2
2^n/an=2^(n-n+2)*2/n(n-1)=8/n(n-1)
lim(2^2/a2+2^3/a3+...+2^n/an)=lim8(1/2*1+1/3*2+1/4*3……+1/n(n-1))
=lim8((1-1/2)+(1/2-1/3)+(1/3-1/4)+……+(1/(n-1)-1/n))=lim8(1-1/n)
(列项求和法)
n→+∞ 1/n→0,lim8(1-1/n)=8