已知函数f（x）=x-ln(x+1),求证2+2/3+2/5+······2/2n-1-ln(2n+1)

数学之美团为你解答令 g(x) = x - ln(x+1) - 1/2 x²g'(x) = 1 - 1/(x+1) - x = - x² / (x+1) < 0g(x)为减函数当 x>0时,g(x) < g(0) = 0即 x - ln(x+1) < 1/2 x²分别令 x = 2 ,2/3 ,2/5 ,……2 - ln3 ...