设f(n)=1/(n+1)+1/(n+2)+.+1/(n+2^n),则f(k+1)-f(k)=要有详细过程_数学解答

设f(n)=1/(n+1)+1/(n+2)+.+1/(n+2^n),则f(k+1)-f(k)=
要有详细过程

人气：165 ℃　时间：2020-03-27 13:24:21

解答

f(k)=1/(k+1)+1/(k+2)+...+1/(k+2^k)f(k+1)=1/(k+2)+1/(k+3)+...+1/(k+2^k)+...+1/[k+1+2^(k+1)]所以：f(k+1)-f(k)=1/(k+1+2^k)+1/(k+2+2^k)+...+1/[k+1+2^(k+1)]-1/(k+1)