先阅读，再答题．阅读：因为12-13=32×3-23×2=12×3．13-14=43×4-34×3=13×414-15=

Question

先阅读，再答题．
阅读：因为 (1)/(2) -(1)/(3) =(3)/(2×3) -(2)/(3×2) =(1)/(2×3) ．
(1)/(3) -(1)/(4) =(4)/(3×4) -(3)/(4×3) =(1)/(3×4)
(1)/(4) -(1)/(5) =(5)/(4×5) -(4)/(5×4) =(1)/(4×5) ，…
将上面的式子反过来，有等式：
(1)/(2×3) =(1)/(2) -(1)/(3)
(1)/(3×4) =(1)/(3) -(1)/(4)
(1)/(4×5) =(1)/(4) -(1)/(5) ，…
（1）根据以上材料，请写出： (1)/(2005×2006) =______；
（2）计算： (1)/(3×4) +(1)/(4×5) +(1)/(5×6) +(1)/(6×7) +(1)/(7×8) +(1)/(8×9) +(1)/(9×10) ．

Answer 1

（1） (1)/(2005×2006) = (1)/(2005) -(1)/(2006) ；

（2）原式= (1)/(3) -(1)/(4) +(1)/(4) -(1)/(5) +(1)/(5) -(1)/(6) +(1)/(6) -(1)/(7) +(1)/(7) -(1)/(8) +(1)/(8) -(1)/(9) +(1)/(9) -(1)/(10) = (1)/(3) -(1)/(10) = (7)/(30) ．