f(x)=2x/1+x,求f(1)+f(2)+.f(100)+f(1/2).+f(100/2)+.f(1/100)+f(1/200)+.+f(100/100)
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f(x)=2x/1+x,求f(1)+f(2)+.f(100)+f(1/2).+f(100/2)+.f(1/100)+f(1/200)+.+f(100/100)
f(x)=2x/1+x,求f(1)+f(2)+.f(100)+f(1/2).+f(100/2)+.f(1/100)+f(1/200)+.+f(100/100)
f(x)=2x/1+x,求f(1)+f(2)+.f(100)+f(1/2).+f(100/2)+.f(1/100)+f(1/200)+.+f(100/100)
是求f(1)+f(2)+...+f(100)+f(1/2)+f(2/2)+...+f(100/2)+...+f(1/100)+f(2/100)+...+f(100/100)是吧,呵呵.
f(x)=2x/(1+x)
f(1/x)=2(1/x)/[1+(1/x)]=2/(1+x)
f(x)+f(1/x)=2x/(1+x)+2/(1+x)=(2x+2)/(1+x)=2,为定值.
f(1)+f(2)+...+f(100)+f(1/2)+f(2/2)+...+f(100/2)+...+f(1/100)+f(2/100)+...+f(100/100)
=[f(1)+f(1/2)+...+f(1/100)]+[f(2)+f(2/2)+...+f(2/100)]+...+[f(100)+f(100/2)+...+f(100/100)]
又
f(1)+f(2)+...+f(100)+f(1/2)+f(2/2)+...+f(100/2)+...+f(1/100)+f(2/100)+...+f(100/100)
+[f(1)+f(1/2)+...+f(1/100)]+[f(2)+f(2/2)+...+f(2/100)]+...+[f(100)+f(100/2)+...+f(100/100)]
=[f(1)+f(1)+f(2)+f(1/2)+...+f(100)+f(1/100)]+[f(1/2)+f(2)+f(2/2)+f(2/2)+...+f(100/2)+f(2/100)]+...+
[f(1/100)+f(100)+f(2/100)+f(100/2)+...+f(100/100)+f(100/100)]
=2×100×100
=20000
因此
f(1)+f(2)+...+f(100)+f(1/2)+f(2/2)+...+f(100/2)+...+f(1/100)+f(2/100)+...+f(100/100)
=20000/2
=10000