4n²-1=(2n-1)(2n+1)
所以
sn=1/1×3＋1/3×5＋1/5×7＋....+1/(2n-1)(2n+1)
=1/2 ×【1-1/3+1/3-1/5+1/5-1/7+....+1/(2n-1)-1/(2n+1)】
=1/2 [1-1/(2n+1)]
=n/(2n+1)
an =1/(4n^2-1)
=1/[(2n-1)(2n+1)]
= (1/2)[1/(2n-1) -1/(2n+1)]
Sn =a1+a2+...+an
=(1/2)[ 1-1/(2n+1)]
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