函数f(x)对任意x属于R,都有f(x)+f(1-x)=1/2.(1)求f(1/2)和f(1/n)+f(n-1/n)(n属于正整数N)的值.(2){an}满足an=f(0)+f(1/n)+f(2/n)+…+f((n-1)/n)+f(1)请证明{an}是等差数列(3)bn=4/(4an-1),Sn=32-16/n,Tn=b1^2+b2^2+b3
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![函数f(x)对任意x属于R,都有f(x)+f(1-x)=1/2.(1)求f(1/2)和f(1/n)+f(n-1/n)(n属于正整数N)的值.(2){an}满足an=f(0)+f(1/n)+f(2/n)+…+f((n-1)/n)+f(1)请证明{an}是等差数列(3)bn=4/(4an-1),Sn=32-16/n,Tn=b1^2+b2^2+b3](/uploads/image/z/6603394-58-4.jpg?t=%E5%87%BD%E6%95%B0f%28x%29%E5%AF%B9%E4%BB%BB%E6%84%8Fx%E5%B1%9E%E4%BA%8ER%2C%E9%83%BD%E6%9C%89f%28x%29%2Bf%281-x%29%3D1%2F2.%EF%BC%881%EF%BC%89%E6%B1%82f%281%2F2%29%E5%92%8Cf%281%2Fn%29%2Bf%28n-1%2Fn%29%EF%BC%88n%E5%B1%9E%E4%BA%8E%E6%AD%A3%E6%95%B4%E6%95%B0N%EF%BC%89%E7%9A%84%E5%80%BC.%EF%BC%882%EF%BC%89%7Ban%7D%E6%BB%A1%E8%B6%B3an%3Df%280%29%2Bf%281%2Fn%29%2Bf%282%2Fn%29%2B%E2%80%A6%2Bf%EF%BC%88%28n-1%29%2Fn%EF%BC%89%2Bf%281%29%E8%AF%B7%E8%AF%81%E6%98%8E%7Ban%7D%E6%98%AF%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%EF%BC%883%EF%BC%89bn%3D4%2F%284an-1%29%2CSn%3D32-16%2Fn%2CTn%3Db1%5E2%2Bb2%5E2%2Bb3)
函数f(x)对任意x属于R,都有f(x)+f(1-x)=1/2.(1)求f(1/2)和f(1/n)+f(n-1/n)(n属于正整数N)的值.(2){an}满足an=f(0)+f(1/n)+f(2/n)+…+f((n-1)/n)+f(1)请证明{an}是等差数列(3)bn=4/(4an-1),Sn=32-16/n,Tn=b1^2+b2^2+b3
函数f(x)对任意x属于R,都有f(x)+f(1-x)=1/2.(1)求f(1/2)和f(1/n)+f(n-1/n)(n属于正整数N)的值.
(2){an}满足an=f(0)+f(1/n)+f(2/n)+…+f((n-1)/n)+f(1)请证明{an}是等差数列(3)bn=4/(4an-1),Sn=32-16/n,Tn=b1^2+b2^2+b3^2+…+bn^2比较Tn和Sn大小
函数f(x)对任意x属于R,都有f(x)+f(1-x)=1/2.(1)求f(1/2)和f(1/n)+f(n-1/n)(n属于正整数N)的值.(2){an}满足an=f(0)+f(1/n)+f(2/n)+…+f((n-1)/n)+f(1)请证明{an}是等差数列(3)bn=4/(4an-1),Sn=32-16/n,Tn=b1^2+b2^2+b3
1、令x=1\2,2f(1/2)=1/2,f(1/2)=1/4
令x=1\n,f(1/n)+f(n-1/n)=1/2
2、由于f(1/n)+f(n-1/n)=1/2,f(2/n)+f(n-2/n)=1/2,f(3/n)+f(n-3/n)=1/2、、、
所以n=2k-1时,an=k/2=(n+1)/4,n=2k时,an=k/2+1/4=(n+1)/4
所以an=(n+1)/4为等差数列
3、bn=4/(4an-1)=4/n
所以Tn=b1^2+b2^2+b3^2+…+bn^2=16*【1^2+(1/2)^2+(1/3)^2+…+(1/n)^2】