已知数列an满足a1=1,且an=2an-1+2^n 1、求证an/2^n是等差数列2、求an的通项公式

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已知数列an满足a1=1,且an=2an-1+2^n1、求证an/2^n是等差数列2、求an的通项公式已知数列an满足a1=1,且an=2an-1+2^n1、求证an/2^n是等差数列2、求an的通项

已知数列an满足a1=1,且an=2an-1+2^n 1、求证an/2^n是等差数列2、求an的通项公式
已知数列an满足a1=1,且an=2an-1+2^n 1、求证an/2^n是等差数列2、求an的通项公式

已知数列an满足a1=1,且an=2an-1+2^n 1、求证an/2^n是等差数列2、求an的通项公式
an/2^n
=(2an-1)/2^n + 1
=(an-1)/2^(n-1)+1
an/2^n - (an-1)/2^(n-1) = 1
则an/2^n是公差为1的等差数列
2.
设Tn=an/2^n
则Tn是公差为1的等差数列
Tn=T1 + (n-1)d=a1/2 + (n-1)*1=n-1/2
则an=(n-1/2)*2^n=n*2^n - 2^(n-1)

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