2009×2011/2010^2-1 Calculated by square difference formula

2009×2011/2010^2-1 Calculated by square difference formula

Original formula =(2010-1)×(2010+1)/(2010^2-1)
=(2010^2-1)/(2010^2-1)
=1

Calculation:1/1*2010+1/2*2009+...+1/2010*1-1010/2011(1/1*2009+1/2*2008+...+1/2009*1=

1/1*2010+1/2*2009+...+1/2010*1-1010/2011(1/1*2009+1/2*2008+...+1/2009*1)
=(1/2011)(1/1+1/2010+1/2+1/2009+...+1/2010+1/1)-(1/2011)(1/1+1/2009+1/2+1/2008+...+1/2009+1/1)
=(1/2011)(1/2010+1/2010)
=2/(2011*2010)
=1/2021055