1-1/k平方=(1+1/k)(1-1/k)=[(k+1)/k][(k-1)/k]
所以2x(1-1/2013平方)x(1-1/2012平方)X(1-1/2011平方)X.X(1-1/2平方)
=2x(2014/2013)x(2012/2013)x(2013/2012)x2011/2012x.x(4/3)x(2/3)x(3/2)x(1/2)
=2x(2014/2013)x(1/2)=2014/2013 注意中间的全部约掉了
k/(k+1)!=(k+1-1)/(k+1)!=(k+1)/(k+1)!-1/(k+1)!=1/k!-/(k+1)!
1/2!+2/3!+3/4!+4/5!+5/6!+6/7!+7/8!+8/9!
=(2-1)/2!+(3-1)/3!+.+(9-1)/9!
=1/1!-1/2!+1/2!-1/3!+.+1/8!-1/9!
=1/1!-1/9!
=1-1/362880=362879/362880