求数列{1⼀(2n-1)(2n+1)}的前n项和Sn.

2025-02-25 20:33:40
推荐回答(1个)
回答1:

1/(2n-1)(2n+1)
=1/2*[1/(2n-1)-1/(2n+1)]

sn=1/2*(1-1/3)+1/2*(1/3-1/5)+....+1/2*[1/(2n-1)-1/(2n+1)]
=1/2*[1-1/3+1/3-1/5+............+1/(2n-1)-1/(2n+1)]
=1/2*[1-1/(2n+1)]
=1/2*2n/(2n+1)
=n/(2n+1)