a=1,b=2,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2006)(b+2006)的值

a=1,b=2,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2006)(b+2006)的值
a=1,b=2,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2006)(b+2006)的值

a=1,b=2,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2006)(b+2006)的值
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2006)(b+2006)
=1/1*2+1/(1+1)(2+1)+1/(1+2)(2+2)+.+1/(1+2006)(2+2006)
=1/1*2+1/2*3+1/3*4+……+1/2007*2008
=1-1/2+1/2-1/3+1/3-1/4+……+1/2007-1/2008
=1-1/2008
=2007/2008

把a与b的值带入，即是：1/2+【1/(2*3)】+【1/(3*4)】......+【1/(2007+2008)】
用拆项法即为：1/2+【1/2-1/3】+【1/3-1/4】+......+【1/2007-1/2008】{拆项前后有变化的地方，我用【】标出了，应该很容易看明白}
=1/2+1/2-1/2008{前后正负的相同数抵消}
=2007/2008