Question

用1/n-1/(n+1)=1 / [n(n+1)]算出下面这道题

1/ [(x+1)(x+3)]+1/ [(x+3)(x+5)]+1/ [(x+5)(x+7)]+......+1/ [(x+2005)(x+2007)]
我对不起国家，我对不起全部热心回答者，在这道题中分子都是2

Answer 1

1/ [(x+1)(x+3)]+1/ [(x+3)(x+5)]+1/ [(x+5)(x+7)]+......+1/ [(x+2005)(x+2007)]
=(1/2){1/(x+1)-1/(x+3)+1/(x+3)-1/(x+5)+1/(x+5)-1/(x+7)+......+1/(x+2005)-1/(x+2007)}
={1/(x+1)-1/(x+2007)}/2
={(x+2007-x-1)/(x+1)(x+2007)}/2
=1003/(x+1)(x+2007)

分子是2的话 把答案都乘以2呗 2006/(x+1)(x+2007)

Answer 2

原式=(1/2)[1/(x＋1)－1/(x＋3)]＋(1/2)[(1/(x＋3)－1/(x＋5)]…＋(1/2)[1/(x＋2005)－1/(x＋2007)]
=(1/2)[1/(x＋1)－1/(x＋2007)]
=1003/[(x＋1)(x＋2007)]

Answer 3

三国