已知数列an的前n项和为Sn,且Sn+an=2-(1/2)的n-1次方,求证数列(2的n次方.an)为等差数列
人气:137 ℃ 时间:2019-11-21 20:33:48
解答
Sn+an=2-(1/2)^(n-1)
Sn+1 +an+1 =2-(1/2)^n
两式相减,得
2an+1-an=(1/2)^n
两边同乘2^n
2^(n+1)*an+1-2^n*an=1
所以数列{2^n*an}为等差数列
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