已知数列an满足a1=4,an=n+1/n-1乘以an-1则an=

已知数列an满足a1=4,an=n+1/n-1乘以an-1则an=
已知数列an满足a1=4,an=n+1/n-1乘以an-1则an=

已知数列an满足a1=4,an=n+1/n-1乘以an-1则an=
由题
a(n)/a(n-1)=(n+1)/(n-1)
a(n-1)/a(n-2)=n/(n-2)
a(n-2)/a(n-3))=(n-1)/(n-3)
……
a(3)/a(2)=4/2
a(2)/a(1)=3/1
将上面的式子相乘,得
a(n)/a1=n(n+1)/2
又,a1＝4
所以,an＝2n(n+1)

an=(n+1)/(n-1)a(n-1)=(n+1)n/(n-1)(n-2) a(n-2)=(n+1)n/(n-2)(n-3) a(n-3)=(n+1)n/(n-3)(n-4) a(n-4)
=...............=(n+1)n/3*2 a2=(n+1)n/2 a1=2(n+1)n

n≥2时，
an=[(n+1)/(n-1)]a(n-1)
an/a(n-1)=(n+1)/(n-1)
a(n-1)/a(n-2)=n/(n-2)
…………
a2/a1=3/1
连乘
an/a1=(3/1)(4/2)...[(n+1)/(n-1)]=[3×4×...×n×(n+1)]/[1×2×...×(n-1)]=n(n+1)/2<...

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n≥2时，
an=[(n+1)/(n-1)]a(n-1)
an/a(n-1)=(n+1)/(n-1)
a(n-1)/a(n-2)=n/(n-2)
…………
a2/a1=3/1
连乘
an/a1=(3/1)(4/2)...[(n+1)/(n-1)]=[3×4×...×n×(n+1)]/[1×2×...×(n-1)]=n(n+1)/2
an=[n(n+1)/2]a1=2n(n+1)=2n²+2n
n=1时，a1=2×1²+2×1=4，同样满足通项公式
数列{an}的通项公式为an=2n²+2n。

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