设f(n)=1+1/2+1/3+...+1/n(n属于N*),则f(2^(k+1))-f(2^k)=大神们帮帮忙

问题描述:

设f(n)=1+1/2+1/3+...+1/n(n属于N*),则f(2^(k+1))-f(2^k)=大神们帮帮忙

f(2^(k+1))-f(2^k) =1/[(2^k)+1]+ 1/[(2^k)+2]+ .+1/[(2^(k+1)] =(2^k){1/[(2^k)+1]+1/[(2^(k+1)]}/2