Question

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?

Answer 1

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)))))