- 已知函数f(x)=4^x/4^x+2:(1)计算f(0.1)+f?
- 已知f(x)=4^x/4^x+2:(1)计算f(0.1)+f(0.9)的值;(2)设数列{An}满足An=f(n/1001),求此数列前1000项的和
-
f(1-x)=4^(1-x)/[4^(1-x)+2]
=[4/4^x/[4/4^x+2]]
=4/(4+2*4^x)
=2/(2+4^x)
f(x)+f(1-x)=1
所以(1)计算f(0.1)+f(0.9)=1
(2)设数列{An}满足An=f(n/1001),求此数列前1000项
S1000=（A1+A1000）+（A2+A999）+……+（A500+A501）
=[f(1/1001)+f(1000/1001)]+[f(2/1001)+f(999/1001)]+……+[f(500/1001)+f(501/1001)]
=500