S=2-2^2+2^3-2^4+2^5-2^6+2^7-2^8+……+2^19-2^20
S=(2-2^2)+(2^3-2^4)+(2^5-2^6)+……+(2^19-2^20)
S=2(1-2)+2^3(1-2)+2^5(1-2)+……+2^19(1-2)
S=-2-2^3-2^5-2^7-2^9-……-2^19---------------(1)
(1)式两边同乘以2^2,得:4S=-2^3-2^5-2^7-2^9-……-2^19-2^21.------(2)
(2)-(1)式,得：3S=-2^21+2,故S=（2-2^21)/3.