1/(1x3)+1/(3x5)+1/(5x7)+……+1/[(2n-1)x(2n+1)]
=(1-1/3)/2+(1/3-1/5)/2+(1/5-1/7)/2+……+[1/(2n-1)-1/(2n+1)]/2
=[1-1/(2n+1)]/2
=n/(2n+1)
∴前N项和为n/(2n+1)
Sn=2(1/1-1/3)+2(1/3-1/5)......2(1/(2n-1)-1/(2n+1))
=2(1-1/2n+1)=4n/(2n+1)
1/(1x3)+1/(3x5)+1/(5x7)+……+1/[(2n-1)x(2n+1)]
=(1-1/3)/2+(1/3-1/5)/2+(1/5-1/7)/2+……+[1/(2n-1)-1/(2n+1)]/2
=[1-1/(2n+1)]/2
=n/(2n+1)
∴前N项和为n/(2n+1)
Sn=2(1/1-1/3)+2(1/3-1/5)......2(1/(2n-1)-1/(2n+1))
=2(1-1/2n+1)=4n/(2n+1)