化简:1+1/n²+1/(n+1)²,并把结果写成一个式子的平方

显示全部楼层 · 2013-3-5 18:10:09

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{a+n}^2 / [n(n+1)]^2={n^2 +1+n}^2 / [n(n+1)]^2={（n^2 +1+n）^2 / [n(n+1)}^2评论|0...

千问 · 2013-3-5 18:10:09

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} ...

千问 · 2013-3-5 18:10:09

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} ...

千问 · 2013-3-5 18:10:09

答案是(N*(N+1)+1/N*(N+1))^2...