化简 √[1+1/n ^2+1/(n+1)^2]

来源：学生作业帮助网编辑：作业帮时间：2024/05/11 05:24:34

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)

[3n(n+1)+n(n+1)(2n+1)]/6+n(n+2)化简 [3n(n+1)+n(n+1)(2n+1)]/6+n(n+2)化简化简n分之n-1+n分之n-2+n分之n-3+.+n分之1 化简n分之n-1+n分之n-2+n分之n-3+.+n分之1 2^n/n*(n+1) 化简：(n+1)!/n!-n!/(n-1)! 化简(n+1)(n+2)(n+3) 证明不等式：(1/n)^n+(2/n)^n+(3/n)^n+.+(n/n)^n 化简[n^2+(n+1)^2]/n(n+1) 化简额 (n+2)!/(n+1)! 化简：1/(n+1)(n+2)+1/(n+2)(n+3)+1/(n+3)(n+4) 已知n属于N,n>=1,f(n)=√(n^2+1)-n,t(n)=1/2n,g(n)=n-√(n^2-1)则f(n),t(n),g(n)的大小关系为? f(x)=e^x-x 求证(1/n)^n+(2/n)^n+...+(n/n)^n n^(n+1/n)/(n+1/n)^n n*【n+1】*【n+2】化简成什么? 2n/（n+1）n! n(n+1)(n+2)等于多少? n+(n-1)÷2×n 求化简