[MukunthFx]

I have attached the question in image format.

Required with Steps please :)

Thanks in Advance :)

[Curlyben]

What do YOU think ?
While we're happy to HELP we wont do all the work for you.
Show us what you have done and where you are having problems..

[ebaines]

OK, this is a pretty tricky problem, so I'll give you a hint to get you started. I assume you are familiar with the technique for determining the values of the continued fraction for a number x = [a_0,; a_1, a_2, a_3, ...]. I am not aware of a general technique for determining the value of x given the values of the a's, especially when there are an infinite number of them, as in this problem. So we're going to have to rely on a trick based on the fact that all the a's are the same value. Given a number x, the value of a_0 is the integer portion of x; in this case we know a_0 = 4. To determine subsequent values of the a's you start by subtracting out a_0 (in this case 4), leaving x-4, then take the inverse of that, yielding 1/(4-x). Let's call this new value x_1. The next term a_1 is the integer portion of x_1. But ask yourself this: what is the continued fraction of x_1? Consider the nature of the initial continued fraction with its infinite sequence of the same value - can you conclude something about the continued fraction of x_1 (and x_2, and x_3 etc.) from the fact that the initial continued fraction is an infinite series where all the a's are the same value?