Question

设f(n)=1+1/2+1/3+...1/n,则f(2^k)变形到f(2^k+1)需要增添项数是多少

Answer 1

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+1)

所以一共多加了 2^（k+1）-2^k =2^k 项