题目

已知1/2=1/1+1/1,2/3=1/1+1/1+1/1,我们称等式右边为连分数,请将8/13写成连分数形式?

提问时间：2021-03-03

答案

已知1/2=1/(1+1/1),
2/3=1/(1+1/(1+1/1)),
.
8/13=1/(13/8)
=1/(1+5/8)
=1/(1+1/(8/5))
=1/(1+1/(1+3/5))
=1/(1+1/(1+1/(5/3)))
=1/(1+1/(1+1/(1+2/3)))
=1/(1+1/(1+1/(1+1/(3/2))))
=1/(1+1/(1+1/(1+1/(1+1/2))))
=1/(1+1/(1+1/(1+1/(1+1/(2/1)))))
=1/(1+1/(1+1/(1+1/(1+1/(1+1/1)))))