f(n)=1+1/2+1/3...+1/n,n=(1,2.),那么f(2^(k+1))-f(2^k)=?
问题描述：
f(n)=1+1/2+1/3...+1/n,n=(1,2.),那么f(2^(k+1))-f(2^k)=?
答
∵f(2^k)=1+1/2+...+1/2^k,f(2^(k+1))=1+1/2+...+1/2^k+1/(2^k+1)+1/(2^k+2)+...+1/2^(k+1)∴f(2^(k+1))-f(2^k)=1/(2^k+1)+1/(2^k+2)+...+1/2^(k+1)[共2^(2+1)-2^k=2^k项].