一道较难的数学题(十)求大神帮助设A(x1,y1),B(x2,y2)是函数f(x)=1/2+log2(x/(1-x))的图像上任意两点,且OM=1/2(OA+OB),(OM,OA,OB均为向量),已知点M的横坐标为1/2.(1)求证:M点的横坐标为定值; (2)若Sn=f(1/n)+f(2/n)+.
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![一道较难的数学题(十)求大神帮助设A(x1,y1),B(x2,y2)是函数f(x)=1/2+log2(x/(1-x))的图像上任意两点,且OM=1/2(OA+OB),(OM,OA,OB均为向量),已知点M的横坐标为1/2.(1)求证:M点的横坐标为定值; (2)若Sn=f(1/n)+f(2/n)+.](/uploads/image/z/10234720-64-0.jpg?t=%E4%B8%80%E9%81%93%E8%BE%83%E9%9A%BE%E7%9A%84%E6%95%B0%E5%AD%A6%E9%A2%98%28%E5%8D%81%29%E6%B1%82%E5%A4%A7%E7%A5%9E%E5%B8%AE%E5%8A%A9%E8%AE%BEA%28x1%2Cy1%29%2CB%28x2%2Cy2%29%E6%98%AF%E5%87%BD%E6%95%B0f%28x%29%3D1%2F2%2Blog2%28x%2F%281-x%29%29%E7%9A%84%E5%9B%BE%E5%83%8F%E4%B8%8A%E4%BB%BB%E6%84%8F%E4%B8%A4%E7%82%B9%2C%E4%B8%94OM%3D1%2F2%28OA%2BOB%29%2C%28OM%2COA%2COB%E5%9D%87%E4%B8%BA%E5%90%91%E9%87%8F%29%2C%E5%B7%B2%E7%9F%A5%E7%82%B9M%E7%9A%84%E6%A8%AA%E5%9D%90%E6%A0%87%E4%B8%BA1%2F2.%281%29%E6%B1%82%E8%AF%81%3AM%E7%82%B9%E7%9A%84%E6%A8%AA%E5%9D%90%E6%A0%87%E4%B8%BA%E5%AE%9A%E5%80%BC%3B+%282%29%E8%8B%A5Sn%3Df%281%2Fn%29%2Bf%282%2Fn%29%2B.)
一道较难的数学题(十)求大神帮助设A(x1,y1),B(x2,y2)是函数f(x)=1/2+log2(x/(1-x))的图像上任意两点,且OM=1/2(OA+OB),(OM,OA,OB均为向量),已知点M的横坐标为1/2.(1)求证:M点的横坐标为定值; (2)若Sn=f(1/n)+f(2/n)+.
一道较难的数学题(十)求大神帮助
设A(x1,y1),B(x2,y2)是函数f(x)=1/2+log2(x/(1-x))的图像上任意两点,且OM=1/2(OA+OB),(OM,OA,OB均为向量),已知点M的横坐标为1/2.(1)求证:M点的横坐标为定值; (2)若Sn=f(1/n)+f(2/n)+...+f((n-1)/n),n∈N*,且n≥2,求Sn; (3)已知 2/3 (n=1) an= ,其中n∈N*,T为数列的前n项和,若 1/(Sn+1)
一道较难的数学题(十)求大神帮助设A(x1,y1),B(x2,y2)是函数f(x)=1/2+log2(x/(1-x))的图像上任意两点,且OM=1/2(OA+OB),(OM,OA,OB均为向量),已知点M的横坐标为1/2.(1)求证:M点的横坐标为定值; (2)若Sn=f(1/n)+f(2/n)+.
.(1)证明:∵ ∴M是AB的中点.设M点的坐标为(x,y),由(x1+x2)=x=,得x1+x2=1,则x1=1-x2或x2=1-x1.而y=(y1+y2)= [f(x1)+f(x2)] =(+log2 =(1+log2 =(1+log2 =(1+log2 ∴M点的纵坐标为定值.(2)由(1)知x1+x2=1,f(x1)+f(x2)=y1+y2=1,Sn=f( Sn=f(,两式相加得:2Sn=[f()+[f()+…+[f() = ∴Sn=(n≥2,n∈N*).(2)当n≥2时,an= Tn=a1+a2+a3+…+an=[() =( 由Tn,即λ的取值范围是(+∞).