1、1/2*4+1/4*6+1/6*8+···+1/2008*2010
=1/4(1*1/2+1/2*1/3+1/3*1/4+.+1/1004*1/1005)
=1/4(1-1/2+1/2-1/3+1/3-1/4+...1/1004-1/1005)
=1/4*(1-1/1005)
=1/4*1004/1005
=251/1005
2、设y=ax的17次方+bx的13次方+cx的11次方—5,其中a、b、c为常数,已知当x=-7时,y=7.试求x=7时,y的值是多少?
y=ax^17+bx^13+cx^11—5
y+5=ax^17+bx^13+cx^11
a(-7)^17+b(-7)^13+c(-7)^11=7+5=12
a*7^17+b*7^13+c*7^11=-(a(-7)^17+b(-7)^13+c(-7)^11)=-12
3、计算：
（1/3+1/4+···+1/2001)*(1/2+1/3+····1/2000)—(1/2+1/3+···1/2001)*(1/3+1/4+····+1/2000)
=[(1/3+1/4+···+1/2000)+1/2001]*(1/2+1/3+····1/2000)-[(1/2+1/3+···+1/2000)+1/2001](1/3+1/4+····+1/2000)
=(1/3+1/4+···+1/2000)(1/2+1/3+····1/2000)+1/2001(1/2+1/3+····1/2000)-(1/2+1/3+····1/2000)(1/3+1/4+···+1/2000)-1/2001(1/3+1/4+···+1/2000)
=1/2001(1/2+1/3+····1/2000)-1/2001(1/3+1/4+···+1/2000)
=1/2001*1/2
=1/4002
