解:设2^2+2^3+2^4+2^5+……+2^9=X;-------------(1)
(1)x2,得: 2^3+2^4+2^5+……+2^10=2X.-------(2)
(2)-(1),得:2^10-2^2=X,即:2^2+2^3+2^4+2^5+……+2^9=2^10-2^2.
所以,2-2^2-2^3-2^4-2^5-……-2^9+2^10
=2-(2^2+2^3+2^4+2^5+……+2^9)+2^10
=2-(2^10-2^2)+2^10
=2+2^2
=6.
wenxindefeng6 给出的的方法可取
-2042
6