题目

1.2009/1+2009/2+2009/3+.2009/2008= 2.2/1+4/1+8/1+16/1+.+1024/1=
2009/1+2009/2+2009/3+.2009/2008= 2/1+4/1+8/1+16/1+.+1024/1=

提问时间：2021-03-17

答案

楼主分数写法不对.楼上第2问回答错误,题目是有限数列,不是无限数列.
1.
1/2009+2/2009+3/2009+……+2008/2009
=(1/2009)*(1+2+3+……+2008)
=(1/2009)*{[2008*(2008+1)]/2}
=(1/2009)*(1004*2009)
=1004
2.
1/2+1/4+1/8+1/16+……+1/1024
=1/2+(1/2)^2+(1/2)^3+(1/2)^4+……+(1/2)^10
=(1/2)*{[1-(1/2)^10]/(1-1/2)}
=1-(1/2)^10
=1-1/1024
=1023/1024