观察下列各式：√1+1/3＝2√1/3,√2+1/4＝3√1/4,√3+1/5＝4√1/5···.用发现的规律用含n的式子表示
问题描述：
观察下列各式：√1+1/3＝2√1/3,√2+1/4＝3√1/4,√3+1/5＝4√1/5···.用发现的规律用含n的式子表示
答
√(1+1/3)=2√(1/3)，√(2+1/4)=3√(1/4)，√(3+1/5)=4√(1/5)···。
√[n+1/(n+2)]
=√[n(n+2)/(n+2)+1/(n+2)]
=√[(n^2+2n+1)/(n+2)]
=√[(n+1)^2/(n+2)]
=(n+1)√[1/(n+2)]
.
答
答
√﹙n-1﹚ + 1/﹙n+1﹚= n√1/﹙n+1﹚
答
√n+1/(n+2)＝(n+1)√1/(n+2)
答
√[n+1/(n+2)]=(n+1)√(1/n+2)
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答
√n+1/(n+2)=(n+1)√1/(n+2)
答
√[n＋1/﹙n＋2﹚]＝n√[1/﹙n＋2﹚].