形如f(x)=ax的函数满足f(x+y)=f(x)+f(y),
因为f(1)=2,所以f(n)=2n=nf(1)
f(1)+f(2)+...+f(n)
=f(1)+2f(1)+...+nf(1)
=[n(n+1)/2] f(1)
=n(n+1)=f[n(n+1)/2],
应该都可以.
形如f(x)=ax的函数满足f(x+y)=f(x)+f(y),
因为f(1)=2,所以f(n)=2n=nf(1)
f(1)+f(2)+...+f(n)
=f(1)+2f(1)+...+nf(1)
=[n(n+1)/2] f(1)
=n(n+1)=f[n(n+1)/2],
应该都可以.