n!=1*2*3*…*n
1/(1*2)=(2-1)/(1*2)=2/(1*2)-1/(1*2)=1-1/(1*2)=1-1/(2!)
2/(1*2*3)=(3-1)/(1*2*3)=3/(1*2*3)-1/(1*2*3)=1/(1*2)-1/(1*2*3)=1/(2!)-1/(3!)
同理 3/(1*2*3*4)=1/(1*2*3)-1/(1*2*3*4)=1/(3!)-1/(4!)
…………………
9/(10!)=1/(1*2*3*4*5*6*7*8*9)-1/(1*2*3*4*5*6*7*8*9*10)=1/(9!)-1/(10!)
所以原式=1-1/(2!)+1/(!2)-1/(3!)+1/(3!)-1/(4!)+……+1/(9!)-1/(10!)
=1-(1/10!)