求数列{1/(2n-1)(2n+3)}的前n项和Sn分母是(2n-1)(2n+3)

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求数列{1/(2n-1)(2n+3)}的前n项和Sn分母是(2n-1)(2n+3)

求数列{1/(2n-1)(2n+3)}的前n项和Sn分母是(2n-1)(2n+3)
求数列{1/(2n-1)(2n+3)}的前n项和Sn
分母是(2n-1)(2n+3)

求数列{1/(2n-1)(2n+3)}的前n项和Sn分母是(2n-1)(2n+3)
1/(2n-1)(2n+3)=1/4*[1/(2n-1)-1/(2n+3)]
数列{1/(2n-1)(2n+3)}的前n项和
Sn=1/4*[1-1/5+1/3-1/7+1/5-1/9+----------+1/(2n-3)-1/(2n+1)+1/(2n-1)-1/(2n+3)]
=1/4*[1+1/3-1/(2n+1)-1/(2n+3)]
(接下去化简下)

1/(2n-1)(2n+3)=1/4(1/(2n-1)-1/(2n+3))
Sn=1/4(1-1/5+1/3-1/7+1/5-...+1/(2n-3)-1/(2n+1)+1/(2n-1)-1/(2n+3))
=1/4(1+1/3-1/(2n+1)-1/(2n+3))=1/3-1/4(1/(2n+1)+1/(2n+3))