计算1/(3*5)+1/(5*7)+……+1/(2007*2009) 的值

问题描述:

计算1/(3*5)+1/(5*7)+……+1/(2007*2009) 的值

1/(3*5)+1/(5*7)+……+1/(2007*2009)
=(1/3-1/5)÷2+(1/5-1/7)÷2+……+(1/2007-1/2009)÷2
=[(1/3-1/5)+(1/5-1/7)+……+(1/2007-1/2009)]÷2
=(1/3-1/5+1/5-1/7+……+1/2007-1/2009)÷2
中间可以互相抵消
=(1/3-1/2009)÷2
=2006/6027÷2
=1003/6027