B=x^2009 -2009x^2008 +2009x^2007-…+2009x-1 tại x = 2008 . tính B 02/10/2021 Bởi Amaya B=x^2009 -2009x^2008 +2009x^2007-…+2009x-1 tại x = 2008 . tính B
$\begin{array}{l} B = {x^{2009}} – 2009{x^{2008}} + 2009{x^{2007}} – …. + 2009x – 1\\ Ta\,\,co:\,\,\,x = 2008\\ \Leftrightarrow 2009 = 2008 + 1 = x + 1\\ \Rightarrow B = {x^{2009}} – \left( {x + 1} \right){x^{2008}} + \left( {x + 1} \right){x^{2007}} – …. + \left( {x + 1} \right)x – 1\\ = {x^{2009}} – {x^{2009}} – {x^{2008}} + {x^{2008}} + {x^{2007}} – ….. + {x^2} + x – 1\\ = x – 1 = 2008 – 1 = 2007. \end{array}$ Bình luận
$\begin{array}{l}
B = {x^{2009}} – 2009{x^{2008}} + 2009{x^{2007}} – …. + 2009x – 1\\
Ta\,\,co:\,\,\,x = 2008\\
\Leftrightarrow 2009 = 2008 + 1 = x + 1\\
\Rightarrow B = {x^{2009}} – \left( {x + 1} \right){x^{2008}} + \left( {x + 1} \right){x^{2007}} – …. + \left( {x + 1} \right)x – 1\\
= {x^{2009}} – {x^{2009}} – {x^{2008}} + {x^{2008}} + {x^{2007}} – ….. + {x^2} + x – 1\\
= x – 1 = 2008 – 1 = 2007.
\end{array}$