有理数a不等于1,我们把1/(1-a)称为a的差倒数.如:2的差倒数是1/(1-2)=-1,-1的差倒数是1/[1-(-1)]=1/2,如果a1=3,a2是a1的差倒数,a3是a2的差倒数,a4是a3的差倒数,...,依此类推,那么a2013=___.
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![有理数a不等于1,我们把1/(1-a)称为a的差倒数.如:2的差倒数是1/(1-2)=-1,-1的差倒数是1/[1-(-1)]=1/2,如果a1=3,a2是a1的差倒数,a3是a2的差倒数,a4是a3的差倒数,...,依此类推,那么a2013=___.](/uploads/image/z/546015-39-5.jpg?t=%E6%9C%89%E7%90%86%E6%95%B0a%E4%B8%8D%E7%AD%89%E4%BA%8E1%2C%E6%88%91%E4%BB%AC%E6%8A%8A1%2F%281-a%29%E7%A7%B0%E4%B8%BAa%E7%9A%84%E5%B7%AE%E5%80%92%E6%95%B0.%E5%A6%82%EF%BC%9A2%E7%9A%84%E5%B7%AE%E5%80%92%E6%95%B0%E6%98%AF1%2F%281-2%29%3D-1%2C-1%E7%9A%84%E5%B7%AE%E5%80%92%E6%95%B0%E6%98%AF1%2F%5B1-%28-1%29%5D%3D1%2F2%2C%E5%A6%82%E6%9E%9Ca1%3D3%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...%2C%E4%BE%9D%E6%AD%A4%E7%B1%BB%E6%8E%A8%2C%E9%82%A3%E4%B9%88a2013%3D___.)
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有理数a不等于1,我们把1/(1-a)称为a的差倒数.如:2的差倒数是1/(1-2)=-1,-1的差倒数是1/[1-(-1)]=1/2,如果a1=3,a2是a1的差倒数,a3是a2的差倒数,a4是a3的差倒数,...,依此类推,那么a2013=___.
有理数a不等于1,我们把1/(1-a)称为a的差倒数.
如:2的差倒数是1/(1-2)=-1,-1的差倒数是1/[1-(-1)]=1/2,如果a1=3,a2是a1的差倒数,a3是a2的差倒数,a4是a3的差倒数,...,依此类推,那么a2013=___.
有理数a不等于1,我们把1/(1-a)称为a的差倒数.如:2的差倒数是1/(1-2)=-1,-1的差倒数是1/[1-(-1)]=1/2,如果a1=3,a2是a1的差倒数,a3是a2的差倒数,a4是a3的差倒数,...,依此类推,那么a2013=___.
a2=a1的差倒数是1/(1-3)=-1/2
a3=a2的差倒数是1/(1+1/2)=2/3
a4=a3的差倒数是1/(1-2/3)=3
a1=3 a2=-1/2 a3=2/3 a4=3
而2013/3=671 所以 a2013=2/3.
a1=3 a2=-1/2 a3=2/3 a4=3
所以3个一循环。。
2013除以3等于671.。可以整除。。所以a2013=a3=2/3