设f(x)=4^x/(4^x+2)求f(1/1001)+f(2/1001)+……+f(1000/1001)的值
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设f(x)=4^x/(4^x+2)求f(1/1001)+f(2/1001)+……+f(1000/1001)的值
设f(x)=4^x/(4^x+2)求f(1/1001)+f(2/1001)+……+f(1000/1001)的值
设f(x)=4^x/(4^x+2)求f(1/1001)+f(2/1001)+……+f(1000/1001)的值
f(x)+f(1-x)
=4^x/(4^x+2)+4^(1-x)/[4^(1-x)+2]
=4^x/(4^x+2)+(4/4^x)/[(4/4^x)+2]
=4^x/(4^x+2)+4/(4+2*4^x)
=4^x/(4^x+2)+2/(2+4^x)
=(4^x+2)/(4^x+2)
=1
所以f(1/1001)+f(2/1001)+……+f(1000/1001)
=[f(1/1001)+f(1000/1001)]+……+[f(500/1001)+f(501/1001)]
=1+1+……+1
=1*500
=500
1.f(x-1)=(4^x/4)/(4^x/4+2)
上下全部乘上4
因此f（x-1）=4^x/(4^x+8）
设y=4^x
f(x)+f(x-1）=y/(y+2)+y/(y+8)=2y(y+5)/(y+2)(y+8)
将y=4^x代入后也没办法化简。
2.f(x)=4^x/(4^x+2)
f(x-1)=4^(x-1)/(4^(x-1)+2)
f(x)+f(x-1)=4^x/(4^x+2)+4^(x-1)/(4^(x-1)+2)
由题意易证
f(x)+f(1-x)
=4^x/(4^x+2)+4^(1-x)/(4^(1-x)+2)
=4^x/(4^x+2)+2/(4^x+2)
=1
所以f(1/1001)+f(2/1001)+……+f(1000/1001)=500
当a+b=1时 f(a)+f(b)=1 用通分证明.
所以f(1/1001)+f(2/1001)+……+f(1000/1001)分组求和..
值为500