For real number a,let[a]denote the
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For real number a,let[a]denote the maximum integer which does not exceed a.For example,[3.1]=3,[-1.5]=-2,[0.7]=0 Now let f(x)=(x+1)/(x-1),then[f(2)]+[f(3)]+…+[f(100)]=______.(英汉小词典real number:实数;the maximum integer which does not exceed a:不超过a的最大整数)
∵f(x)=x+1x−1,∴f(2)=2+12−1=3,f(3)=3+13−1=2,f(4)=4+14−1=53,f(5)=5+15−1=32,…f(100)=100+1100−1=10199,∴[f(2)]=3,[f(3)]=2,[f(4)]=[f(5)]=…[f(100)]=1,∴[f(2)]+[f(3...