定义:a是不为1的有理数.定义:a是不为1的有理数,我们把1/1-a称为a的倒差数.如:2的倒差数是1/1-2=-1,-1的差倒数是1/1-(-1)=1/2.已知a1=1/3,a2是a1的差倒数,a3是a2的差倒数,a4是a3的差倒数,...以此类推,
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![定义:a是不为1的有理数.定义:a是不为1的有理数,我们把1/1-a称为a的倒差数.如:2的倒差数是1/1-2=-1,-1的差倒数是1/1-(-1)=1/2.已知a1=1/3,a2是a1的差倒数,a3是a2的差倒数,a4是a3的差倒数,...以此类推,](/uploads/image/z/5322848-32-8.jpg?t=%E5%AE%9A%E4%B9%89%3Aa%E6%98%AF%E4%B8%8D%E4%B8%BA1%E7%9A%84%E6%9C%89%E7%90%86%E6%95%B0.%E5%AE%9A%E4%B9%89%3Aa%E6%98%AF%E4%B8%8D%E4%B8%BA1%E7%9A%84%E6%9C%89%E7%90%86%E6%95%B0%2C%E6%88%91%E4%BB%AC%E6%8A%8A1%2F1-a%E7%A7%B0%E4%B8%BAa%E7%9A%84%E5%80%92%E5%B7%AE%E6%95%B0.%E5%A6%82%EF%BC%9A2%E7%9A%84%E5%80%92%E5%B7%AE%E6%95%B0%E6%98%AF1%2F1-2%3D-1%2C-1%E7%9A%84%E5%B7%AE%E5%80%92%E6%95%B0%E6%98%AF1%2F1-%EF%BC%88-1%EF%BC%89%3D1%2F2.%E5%B7%B2%E7%9F%A5a1%3D1%2F3%2Ca2%E6%98%AFa1%E7%9A%84%E5%B7%AE%E5%80%92%E6%95%B0%2Ca3%E6%98%AFa2%E7%9A%84%E5%B7%AE%E5%80%92%E6%95%B0%2Ca4%E6%98%AFa3%E7%9A%84%E5%B7%AE%E5%80%92%E6%95%B0%2C...%E4%BB%A5%E6%AD%A4%E7%B1%BB%E6%8E%A8%2C)
定义:a是不为1的有理数.定义:a是不为1的有理数,我们把1/1-a称为a的倒差数.如:2的倒差数是1/1-2=-1,-1的差倒数是1/1-(-1)=1/2.已知a1=1/3,a2是a1的差倒数,a3是a2的差倒数,a4是a3的差倒数,...以此类推,
定义:a是不为1的有理数.
定义:a是不为1的有理数,我们把1/1-a称为a的倒差数.如:2的倒差数是1/1-2=-1,-1的差倒数是1/1-(-1)=1/2.已知a1=1/3,a2是a1的差倒数,a3是a2的差倒数,a4是a3的差倒数,...以此类推,则a2,a3,a4,a2009是多少?
请说出解题思路!
定义:a是不为1的有理数.定义:a是不为1的有理数,我们把1/1-a称为a的倒差数.如:2的倒差数是1/1-2=-1,-1的差倒数是1/1-(-1)=1/2.已知a1=1/3,a2是a1的差倒数,a3是a2的差倒数,a4是a3的差倒数,...以此类推,
a1=1/3
a2=1/(1-a1)=3/2
a3=1/(1-a2)=1/(1-3/2)=-2
a4=1/(1-a3)=1/(1+2)=1/3
a4值又回到了a1值上,以后往复循环,循环周期为3
当n=3k+1时,an=1/3;当n=3k+2时,an=3/2;当n=3k时,an=-2
2009 被3除余2,属于3k+2型,所以a2009=3/2