由 danny 於 星期一 七月 25, 2011 4:16 am
lim [(n+2)*(n+4)*...*(n+2n)]1/n / n
=lim [(1+2/n)*(1+4/n)*...*(1+2n/n)]1/n
=exp(ln(1+2/n)/n+ln(1+4/n)/n+...+ln(1+2n/n)/n)
=exp(Σ(ln(1+2*k/n)/n))
=∫e^(ln(1+2x))dx from 0 to 1
=2
(the red part is right riemann sum,and {[0,1/n],[0,2/n],...,[0,n/n]} is a pratition of [0,1])