1-n(n+1)/(4n^2+4n+1)=3/4+[1/4-n(n+1)/(4n^2+4n+1)]=3/4+[(4n^2+4n+1)-4n(n+1)]/[4(4n^2+4n+1)]=3/4+(4n^2+4n+1-4n^2-4n)/[4(4n^2+4n+1)]=3/4+1/[4(4n^2+4n+1)]=3/4+(1/4)[1/(2n+1)^2]>3/4+(1/4)/[(2n+1)(2n+3)]。
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