函数f(x)满足关系式f(xy)=f(x)+f(y)求f(1/3)+f(1/2)+f(1)+f(2)+f(3)
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函数f(x)满足关系式f(xy)=f(x)+f(y)求f(1/3)+f(1/2)+f(1)+f(2)+f(3)
函数f(x)满足关系式f(xy)=f(x)+f(y)求f(1/3)+f(1/2)+f(1)+f(2)+f(3)
函数f(x)满足关系式f(xy)=f(x)+f(y)求f(1/3)+f(1/2)+f(1)+f(2)+f(3)
设x=1,y=1带入f(xy)=f(x)+f(y)
得f(1)=2f(1),所以f(1)=0
f(1/3)+f(1/2)+f(1)+f(2)+f(3)
=f(1/3)+f(3)+f(1)+f(1/2)+f(2)
=f(1)+f(1)+f(1)
=0
由关系式f(xy)=f(x)+f(y)得
f(1/3)+f(3)=f(1)
f(1/2)+f(2)=f(1)
由题意的f(1)=f(1)+f(1)=2f(1)
故f(1)=0
则f(1/3)+f(1/2)+f(1)+f(2)+f(3)=0
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