(1)
与式=(1-1/3)+(1/3-1/7)+(1/7-1/13)
+(1/13-1/21)
=1-1/21
=20/21
(2)
与式=(2000+1)(2000-1)
+(2000+1)^2-(2000+2)(2000-2)-(2000-2)^2
=(2000^2-1)-(2000^2-4)+
{(2000+1)+(2000-2)}{(2000+1)-(2000-2)}
=(-1+4)+(4000-1)•3
=4000•3
=12000
(3)
与式={(b+c)+a}{(b+c)-a}
+{a-(b-c)}{a+(b-c)}
={(b+c)^2-a^2}
+{a^2-(b-c)^2}
=(b+c)^2-(b-c)^2
=4bc
(4)
与式=(x+1)(x-6)•(x-2)(x-3)
={(x^2-5x)-6}{(x^2-5x)+6}
=(x^2-5)^2-6^2
=x^4-10x^2-11
(5)
与式={(√2-1)(√2+1)}^18
•(√2+1)^2x{(3+2√2)(3-2√2)}^19•(3-2√2)^2
=1•(√2+1)^2x1•(3-2√2)^2
=(3+2√2)(3-2√2)•(3-2√2)
=(9-8)(3-2√2)
=3-2√2
(6)
与式={(√5+√10)^2+2(√5+√10)
•(1/√5)+1/5}+{(√5+√10)^2
-4(√5+√10)•(1/√5)+4/5}
-2(√5+√10)^2
=-2(1+√2)+1/5+4/5
=-1-2√2
