x+1乘x+3分之2 x+3x+5分之2 x+5乘x+7分之2 略去 x+2005乘x+2007分之2 结果多少?要过程_数学解答

x+1乘x+3分之2 x+3x+5分之2 x+5乘x+7分之2 略去 x+2005乘x+2007分之2 结果多少?要过程

人气：128 ℃　时间：2020-06-14 01:47:37

解答

2/[(x+1)(x+3)]+2/[(x+3)(x+5)]+2/[(x+5)(x+7)]+.+2/[(x+2005)(x+2007)]
=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)
=[(x+2007)-(x+1)]/[(x+1)(x+2007)]
=2006/[(x+1)(x+2007)]