数列{An}满足a1=1,且An=2An-1+2^n(n大于等于2且n属于整数).求数列的通项公式如题
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数列{An}满足a1=1,且An=2An-1+2^n(n大于等于2且n属于整数).求数列的通项公式如题数列{An}满足a1=1,且An=2An-1+2^n(n大于等于2且n属于整数).求数列的通项公式
数列{An}满足a1=1,且An=2An-1+2^n(n大于等于2且n属于整数).求数列的通项公式如题
数列{An}满足a1=1,且An=2An-1+2^n(n大于等于2且n属于整数).求数列的通项公式
如题
数列{An}满足a1=1,且An=2An-1+2^n(n大于等于2且n属于整数).求数列的通项公式如题
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.
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)
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。
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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