Derive the inequality $b_{2r-2}≥ 1+b_1+b_2+...+b_{2r-3}$ where $b_{2r} =m_{2r+2}/m_{2r+1}$ and $b_{2r+1} =(m_{2r}+3m_3)/m_{2r+3}$
I know that $b_2≥b_1+1$ and determinant of the matrix $((m_{ij}))≥0$, $m_{ij}=$central moment of order $(i+j)$ but can not proceed further.