数列an满足an+1-an=3*2^2n-1 a1=2 求an通项bn=nan求bn通项公式
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数列an满足an+1-an=3*2^2n-1 a1=2 求an通项bn=nan求bn通项公式
数列an满足an+1-an=3*2^2n-1 a1=2 求an通项
bn=nan求bn通项公式
数列an满足an+1-an=3*2^2n-1 a1=2 求an通项bn=nan求bn通项公式
a(n+1)-an=3*2^(2n-1)
所以:
an-a(n-1)=3*2^(2n-3)
...
a3-a2=3*2^3
a2-a1=3*2^1
上述各项相加:
an-a1=3[2^1+2^3+2^5+2^7+...+2^(2n-3)]
=3*2*[2^(2n-2)-1]/(2^2-1)
=2^(2n-1)-2
因此:
an=2^(2n-1)
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