>>440
logf(x)=(1/n)Σ[k=1,n] log{1+(k/n)}

lim_[n→∞]logf(x)
=∫[0,1] log(1+x)
=[(x+1)log(x+1)-x][0,1]
=2log2-1
=log(4/e)

lim_[n→∞]f(x)=4/e