“1/3*7”应该是“1/5*7”吧
1/1*3+1/3*5+1/5*7+1/7*9+1/9*11
=1/2*(1-1/3)+1/2*(1/3-1/5)+1/2*(1/5-1/7)+1/2*(1/7-1/9)+1/2*(1/9-1/11)
=1/2*(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11)
=1/2*(1-1/11)
=1/2*10/11
=5/11为什么1/2哪来的减号哪来的？1/1*3=1/31/2*(1-1/3)=1/2*2/3=1/3所以1/1*3=1/2*(1-1/3)同理1/3*5=1/151/2*(1/3-1/5)=1/2*2/15=1/151/3*5=1/2*(1/3-1/5)……这叫做列项法