化简 √[1+1/n ^2+1/(n+1)^2]

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化简√[1+1/n^2+1/(n+1)^2]化简√[1+1/n^2+1/(n+1)^2]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+

化简 √[1+1/n ^2+1/(n+1)^2]
化简 √[1+1/n ^2+1/(n+1)^2]

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(n+1)]^2
={a^2 +2an +n^2} / [n(n+1)]^2
={a+n}^2 / [n(n+1)]^2
最后得出：
根号[1 +1/n^2 +1/(n+1)^2]
=(a+n)/n(n+1)
=(n^2 +n+1)/n(n+1)

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