Tính A=xy+x^2y^2+x^4y^4+x^6y^6+...+x^2016y^2016+x^2018y^2018 tại x=−2,y=1/2.

Ta có \(xy = \left( { - 2} \right) \cdot \frac{1}{2} = - 1\).

Khi đó \(A = xy + {x^2}{y^2} + {x^4}{y^4} + {x^6}{y^6} + {x^8}{y^8} + ... + {x^{2016}}{y^{2016}} + {x^{2018}}{y^{2018}}\)

\[ = xy + {\left( {xy} \right)^2} + {\left( {xy} \right)^4} + {\left( {xy} \right)^6} + ... + {\left( {xy} \right)^{2016}} + {\left( {xy} \right)^{2018}}\]

\[ = \left( { - 1} \right) + {\left( { - 1} \right)^2} + {\left( { - 1} \right)^4} + {\left( { - 1} \right)^6} + ... + {\left( { - 1} \right)^{2016}} + {\left( { - 1} \right)^{2018}}\]

\({\rm{ = }} - 1 + 1 + 1 + 1 + ... + 1 + 1 = 1\,\,007\).