定义:a是不为1的有理数,我们把1/a-1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.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,求a2009的值.
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/16 18:55:25
![定义:a是不为1的有理数,我们把1/a-1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.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,求a2009的值.](/uploads/image/z/1106193-57-3.jpg?t=%E5%AE%9A%E4%B9%89%EF%BC%9Aa%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%2Fa-1%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%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%3D-1%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%E2%80%A6%E2%80%A6%E4%BB%A5%E6%AD%A4%E7%B1%BB%E6%8E%A8%2C%E6%B1%82a2009%E7%9A%84%E5%80%BC.)
x]J@⻓LgV c("IŢPP[h|ikE>eIZh4aι7djA]jIH.4=7po2(?JDKX2}=}0tSA
Ccʎ Eϼ=´^4JUvxL4
-է3g
L Zu֑8akA7(Es{>
Fd>Ms*5$+-q-㢒̓df= (G50BR=IWpTwWO
定义:a是不为1的有理数,我们把1/a-1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.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,求a2009的值.
定义:a是不为1的有理数,我们把1/a-1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.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,求a2009的值.
定义:a是不为1的有理数,我们把1/a-1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.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,求a2009的值.
a1=-1/3
a2=1/(1-(-1/3))=3/4
a3=1/(1-3/4)=4
a4=1/(1-4)=-1/3=a1(看好,这是一个循环,逢3一个循环)
也就是a1=a4=a7=a10=.
a2=a5=a8=a11=.
.
那么a2009=a(669x3+2)=a2=3/4