化简 √[1+1/n ^2+1/(n+1)^2]

问题描述:

化简 √[1+1/n ^2+1/(n+1)^2]

先看根号里面的式子:1+1/n^2+1/(n+1)^2={[n(n+1)]^2 +(n+1)^2 +n^2}/ [n(n+1)]^2={(n^2 +1)*(n+1)^2 +n^2}/ [n(n+1)]^2={(n^2 +1)*(n^2 +2n+1)^2 +n^2}/ [n(n+1)]^2令 n^2 +1=a则 原式可化为={a*(a+2n)+n^2} / [n...