数列{an}满足a1=1/2,an+1=1/2-an(n属于正整数)设bn=1/1-an,证明{bn}是等差数列,并求bn和an各位哥哥姐姐们谁会啊?
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数列{an}满足a1=1/2,an+1=1/2-an(n属于正整数)设bn=1/1-an,证明{bn}是等差数列,并求bn和an各位哥哥姐姐们谁会啊?数列{an}满足a1=1/2,an+1=1/2-a
数列{an}满足a1=1/2,an+1=1/2-an(n属于正整数)设bn=1/1-an,证明{bn}是等差数列,并求bn和an各位哥哥姐姐们谁会啊?
数列{an}满足a1=1/2,an+1=1/2-an(n属于正整数)
设bn=1/1-an,证明{bn}是等差数列,并求bn和an
各位哥哥姐姐们谁会啊?
数列{an}满足a1=1/2,an+1=1/2-an(n属于正整数)设bn=1/1-an,证明{bn}是等差数列,并求bn和an各位哥哥姐姐们谁会啊?
an+1=1/2-an两边减1得:
(an+1)-1=1/(2-an)-1,再取倒数整理得:
1/[(an+1)-1]=-1+1/(an-1),
所以,数列{1/[(an)-1]}是首项-2,公差-1的等差数列,∴1/[(an)-1]=-n-1,
解得:an=n/(n+1).
∵bn=1/1-an,代入an整理得:bn=n+1,故bn+1=n+2,(bn+1)-bn=n+2-n-1=1,∴{bn}是等差数列.
下标易混,注意识别.自己写一写更清楚.
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