已知f(x)=ax-ln(-x)……证明:2^0/(2^0+1)+2^1/(2^1+1)+2^2/(2^2+1)+……+2^(n-1)/(2^(n-1)+1)>ln((2^n+1)/2),n为正整数.
问题描述：
已知f(x)=ax-ln(-x)……证明:2^0/(2^0+1)+2^1/(2^1+1)+2^2/(2^2+1)+……+2^(n-1)/(2^(n-1)+1)>ln((2^n+1)/2),n为正整数.
答
可以验证n=1,2时满足.假设当n=k时,2^0/(2^0+1)+2^1/(2^1+1)+2^2/(2^2+1)+……+2^(k-1)/(2^(k-1)+1)>ln((2^k+1)/2)则当n=k+1时,2^0/(2^0+1)+2^1/(2^1+1)+2^2/(2^2+1)+……+2^(k-1)/(2^(k-1)+1) + 2^k/(2^k+1...