计算：S=根号(1+1/1^2+1/2^2)+根号(1+1/2^2+1/3^2)+根号(1+1/3^2+1/4^2)+)+)计算：S=根号(1+1/1^2+1/2^2)+根号(1+1/2^2+1/3^2)+根号(1+1/3^2+1/4^2)+……+根号(1+1/2007^2+1/2008^2)不要复制别人的,要步骤,谢谢了!

Question

计算：S=根号(1+1/1^2+1/2^2)+根号(1+1/2^2+1/3^2)+根号(1+1/3^2+1/4^2)+)+)
计算：S=根号(1+1/1^2+1/2^2)+根号(1+1/2^2+1/3^2)+根号(1+1/3^2+1/4^2)+……+根号(1+1/2007^2+1/2008^2)
不要复制别人的,要步骤,谢谢了!

Answer 1

根号[1+1/n^2+1/(n+1)^2]
=根号[n^2(n+1)^2+n^2+(n+1)^2]/[n(n+1)]
=根号[n^2(n+1)^2+n^2+(n+1)^2]/[n(n+1)]
=根号[(1 + n + n^2)^2]/[n(n+1)]
=(1 + n + n^2)/[n(n+1)]
=1+1/n-1/(n+1)
S
=1+1/1-1/2+1+1/2-1/3+...+1+1/2007-1/2008
=2007+1-1/2008
=2007+2007/2008