Let `f(x)=x+1/(2x+1/(2x+1/(2x+oo)))` Compute the value of `f(50)dotf^(prime)(50)`

Explanation

To solve the problem, we need to compute the value of \( f(50) \cdot f'(50) \) for the function defined as:

\[ f(x) = x + \frac{1}{2x + \frac{1}{2x + \frac{1}{2x + \ldots}}} \]

### Step 1: Define the function
We start by rewriting the function \( f(x) \) in a more manageable form. We can denote the infinite nested fraction as \( y \):
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