lim (n趋近正无穷) cos x /2cosx/4…cosx/2^n

因cos x /2cosx/4…cosx/2^n
=[cosx/2*cosx/4*。*2sinx/2^n*cosx/2^n]/(2sinx/2^n)
=[cosx/2*cosx/4*。。。*sinx/2^(n-1)]/(2sinx/2^n)
=(cosx/2sinx/2)/[2^(n-1)*sin(x/2^n]
=sinx/[2^n*sin(x/2^n)]
所以lim (n趋近正无穷) cos x /2cosx/4…cosx/2^n
=lim (n趋近正无穷) sinx/[x*sin(x/2^n)/(x/2^n)]
=(sinx)/x