Proving a=d: Conditional Identity

[rama]

1. The pratement, all variables and given/known data
If a =1÷(1-b) ,b=1÷(1-c),c=1÷(1-d) prove that a=d

Homework Equations

The Attempt at a Solution

a=1÷(1-b)
a-1÷(1-b)=0
{a(1-b)-1)}÷1-b=0
a-ab-1=0
a-ab=1
similarly
b-bc=1
c-cd=1
could any of you please give a hint, this was on test for 4 marks

 

[pasmith]

1. The pratement, all variables and given/known data
If a =1÷(1-b) ,b=1÷(1-c),c=1÷(1-d) prove that a=d

Homework Equations

The Attempt at a Solution

a=1÷(1-b)
a-1÷(1-b)=0
{a(1-b)-1)}÷1-b=0
a-ab-1=0
a-ab=1
similarly
b-bc=1
c-cd=1
could any of you please give a hint, this was on test for 4 marks

You are given
$$b = \frac{1}{1 - c} = \frac{1}{1 - \frac{1}{1 - d}}$$
Simplify the right hand side and then use
$$a = \frac{1}{1 - b}.$$

 

[rama]

pasmith thanks for your time I finally got it
actually I hesitated to post such easy problems (for this PF level)
good to see you taking time on helping me
by the way how do you write fractions?

 

[adjacent]

Use Latex
Click on the sigma sign on the Advanced editor for references.
Use two #s around the code.
For example \frac{1}{2} and putting two #s around will give $\frac{1}{2}$
If you want to see what others used,right click on the rendered Latex code,>Show Math as> Tex commands.
Pasmith used this Code:
b = \frac{1}{1 - c} = \frac{1}{1 - \frac{1}{1 - d}}