已知函数f(x)对任意xy属于R,总有f(x+y)=f(x)+f(y),化简f(1/2)+f(2/3)+f(3/4)+.f(200_数学解答

已知函数f(x)对任意xy属于R,总有f(x+y)=f(x)+f(y),化简f(1/2)+f(2/3)+f(3/4)+.f(2008/2009)

人气：144 ℃　时间：2020-07-17 19:51:21

解答

f(x+y)=f(x)+f(y)f(x+0)=f(x)+f(0)f(0)=0f(x+(-x))=f(x)+f(-x)=0f(-x)=-f(x)f(2x)=f(x+x)=2f(x)f(x)=(1/2)f(2x)f(1/2)=(1/2)f(1)同理：f(1/3)=(1/3)f(1)...f(1/n)=(1/n)f(1）f(n/(n+1))=f(1-(1/(n+1)))=f(1)+f(-1/(n...