(2n+1)²-(2n-1)²=4n²+4n+1-(4n²-4n+1)=8n
an=[(2n+1)²-(2n-1)²]/[(2n-1)²(2n+1)²]
=(2n+1)²/[(2n-1)²(2n+1)²]-(2n-1)²/[(2n-1)²(2n+1)²]
=1/(2n-1)²-1/(2n+1)²
Sn=a1+a2+a3+……a(n-1)+an
=(1/1²-1/3²)+(1/3²-1/5²)+(1/5²-1/7²)+……+[1/(2n-3)²-1/(2n-1)²]+[1/(2n-1)²-1/(2n+1)²]
=1-[1/(2n+1)²]
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