1/(a+1)(a+3)+1/(a+3)(a+5)+1/(a+5)(a+7)...+1/(a+2003)(a+2005)
因为:1/(a+1)(a+3)=1/2*(1/(a+1)-1/(a+3))
1/(a+3)(a+5)=1/2*(1/(a+3)-1/(a+5))
。。。。。。。。。。
1/(a+2003)(a+2005)=1/2*(1/(a+2003)-1/(a+2005))
所以:1/(a+1)(a+3)+1/(a+3)(a+5)+1/(a+5)(a+7)。 。。+1/(a+2003)(a+2005)
=1/2*(1/(a+1)-1/(a+3)+1/(a+3)-1/(a+5))+。。。。。。。。。。。+1/(a+2003)-1/(a+2005))=1/2*(1/(a+1)-1/(a+2005))。全部
因为:1/(a+1)(a+3)=1/2*(1/(a+1)-1/(a+3))
1/(a+3)(a+5)=1/2*(1/(a+3)-1/(a+5))
。。。。。。。。。。
1/(a+2003)(a+2005)=1/2*(1/(a+2003)-1/(a+2005))
所以:1/(a+1)(a+3)+1/(a+3)(a+5)+1/(a+5)(a+7)。
。。+1/(a+2003)(a+2005)
=1/2*(1/(a+1)-1/(a+3)+1/(a+3)-1/(a+5))+。。。。。。。。。。。+1/(a+2003)-1/(a+2005))=1/2*(1/(a+1)-1/(a+2005))。收起