(1)化简根式项中1+1/(n)^2+1/(n+1)^2的结果

题目

(1)化简根式项中1+1/(n)^2+1/(n+1)^2的结果
(2)根据(1)的计算结果计算根式项中1+1/(1)^2+1/(2)^2+根式项中1+1/(2)^2+1/(3)^2+根式项中1+1/(3)^2+1/(4)^2+…+根式项中1+1/(2007)^2+1/(2008)^2

答案

1+1/(n)^2+1/(n+1)^2
=(1+1/n)^2-2/n+1/(n+1)^2
=(1+1/n)^2-2*(1+1/n)*1/(n+1)+1/(n+1)^2
=(1+1/n-1/(n+1))^2
所以
(1)的答案为1+1/n-1/(n+1)
（2）所求=1+1/1-1/2+1+1/2-1/3+...+1+1/2007-1/2008=2008+1-1/2008