絕對值項(xiàng)恒非負(fù),兩絕對值項(xiàng)之和=0,兩絕對值項(xiàng)分別=0
x-1=0x=1
y-3=0y=3
y=x+2
1/(xy)+1/[(x+2)(y+2)]+1/[(x+4)(y+4)]+...+1/[(x+2010)(y+2010)]
=1/[x(x+2)]+1/[(x+2)(x+4)]+1/[(x+4)(x+6)]+...+1/[(x+2010)(x+2012)]
=(1/2)[1/x -1/(x+2)+1/(x+2)-1/(x+4)+1/(x+4)-1/(x+6)+...+1/(x+2010)-1/(x+2012)]
=(1/2)[1/x -1/(x+2012)]
=(1/2)[1/1 -1/(1+2012)]
=(1/2)(1-1/2013)
=1006/2013

老師扣你分的原因是你算錯(cuò)了.1/[n(n+2)]=(1/2)[1/n -1/(n+2)]而不是1/[n(n+2)]=1/n -1/(n+2)1/[n(n+2)]=(1/2)[1/n -1/(n+2)]，為什么要乘1/2