1/3+1/15+1/35+……+1/323+1/399
=1/(1×3)+1/(3×5)+1/(5×7)+……+1/(17×19)+1/(19×21)
=1/2×(1-1/3)+1/2×(1/3-1/5)+1/2×(1/5-1/7)+……+1/2×(1/17-1/19)+1/2×(1/19-1/21)
=1/2×(1-1/3+1/3-1/5+1/5-1/7+……+1/17-1/19+1/19-1/21)
=1/2×(1-1/21)
=1/2×20/21
=10/21
明白请采纳,有疑问请追问!
有新问题请求助,谢谢!