作业帮先观察下列等式,(1)根号[1+1/(2^2)+1/(2^2)]=1+1/1-1/(1+1)=1又1/2(2)根号[1+1/(2^2)+1/(3^2)]=1+1/2-1/(2+1)=1又1/6(3)根号[1+1/(3^2)+1/(4^2)]=1+1/3-1/(3+1)=1又1/12（1）根据上面三个等式提供的信息,请猜想 根号[1+1/(4^2)+1/(
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![先观察下列等式,(1)根号[1+1/(2^2)+1/(2^2)]=1+1/1-1/(1+1)=1又1/2(2)根号[1+1/(2^2)+1/(3^2)]=1+1/2-1/(2+1)=1又1/6(3)根号[1+1/(3^2)+1/(4^2)]=1+1/3-1/(3+1)=1又1/12（1）根据上面三个等式提供的信息,请猜想 根号[1+1/(4^2)+1/(](/uploads/image/z/6899175-63-5.jpg?t=%E5%85%88%E8%A7%82%E5%AF%9F%E4%B8%8B%E5%88%97%E7%AD%89%E5%BC%8F%2C%281%29%E6%A0%B9%E5%8F%B7%5B1%2B1%2F%282%5E2%29%2B1%2F%282%5E2%29%5D%3D1%2B1%2F1-1%2F%281%2B1%29%3D1%E5%8F%881%2F2%282%29%E6%A0%B9%E5%8F%B7%5B1%2B1%2F%282%5E2%29%2B1%2F%283%5E2%29%5D%3D1%2B1%2F2-1%2F%282%2B1%29%3D1%E5%8F%881%2F6%283%29%E6%A0%B9%E5%8F%B7%5B1%2B1%2F%283%5E2%29%2B1%2F%284%5E2%29%5D%3D1%2B1%2F3-1%2F%283%2B1%29%3D1%E5%8F%881%2F12%EF%BC%881%EF%BC%89%E6%A0%B9%E6%8D%AE%E4%B8%8A%E9%9D%A2%E4%B8%89%E4%B8%AA%E7%AD%89%E5%BC%8F%E6%8F%90%E4%BE%9B%E7%9A%84%E4%BF%A1%E6%81%AF%2C%E8%AF%B7%E7%8C%9C%E6%83%B3+%E6%A0%B9%E5%8F%B7%5B1%2B1%2F%284%5E2%29%2B1%2F%28)
先观察下列等式,(1)根号[1+1/(2^2)+1/(2^2)]=1+1/1-1/(1+1)=1又1/2(2)根号[1+1/(2^2)+1/(3^2)]=1+1/2-1/(2+1)=1又1/6(3)根号[1+1/(3^2)+1/(4^2)]=1+1/3-1/(3+1)=1又1/12（1）根据上面三个等式提供的信息,请猜想 根号[1+1/(4^2)+1/(
先观察下列等式,
(1)根号[1+1/(2^2)+1/(2^2)]=1+1/1-1/(1+1)=1又1/2
(2)根号[1+1/(2^2)+1/(3^2)]=1+1/2-1/(2+1)=1又1/6
(3)根号[1+1/(3^2)+1/(4^2)]=1+1/3-1/(3+1)=1又1/12
（1）根据上面三个等式提供的信息,请猜想 根号[1+1/(4^2)+1/(5^2)] 的结果,并进行验证；
（2）请按照上面等式反映的规律,试写出用n(n为正整数)表示的等式.并进行验证；
先观察下列等式,(1)根号[1+1/(2^2)+1/(2^2)]=1+1/1-1/(1+1)=1又1/2(2)根号[1+1/(2^2)+1/(3^2)]=1+1/2-1/(2+1)=1又1/6(3)根号[1+1/(3^2)+1/(4^2)]=1+1/3-1/(3+1)=1又1/12（1）根据上面三个等式提供的信息,请猜想 根号[1+1/(4^2)+1/(
第一小题你应该会吧,第二小题把n代入到信息中去,步骤和它一样就可以了
数学归纳法验证
根号我打不上： 1+1 n2 +1 (n+1)2 =1+1 n2+n
验证： 1+1 n2 +1 (n+1)2 = n2(n+1)2+(n+1)2+n2 n2(n+1)2
= n2(n+1)2+n2+2n+1+n2 n2(n+1)2
= n2(n+1)2 +2n(n+1)+1 n2(n+1)2
= (n2+n+1)2 n2(n+1)2
=n2+n+1 n(n+1)
=n2+n n2+n +1 n2+n
=1+1 n2+n
第一个：1又1∕20
第二个：1+1∕（n(n+1))