设数列an满足a1=1/2,2nan+1=(n+1)an,求数列an的通项公式

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设数列an满足a1=1/2,2nan+1=(n+1)an,求数列an的通项公式
设数列an满足a1=1/2,2nan+1=(n+1)an,求数列an的通项公式

设数列an满足a1=1/2,2nan+1=(n+1)an,求数列an的通项公式
∵2nan+1=(n+1)an,∴a(n+1)/an=(n+1)/2n,
∴a2/a1=2/2
a3/a2=3/2×2
a4/a3=4/2×3
a5/a4=5/2×4
……
an/a(n-1)=n/2(n-1)
两边分别相乘,得:
an/a1=n/2^n,
∴an=n/2^(n+1).

(2n-2)/n=an-1/an
(2n-4)/n-1=an-2/an-1
.
.
.
2/2=a1/a2
an=a1=1/2

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