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Find the value of
\cfrac{1}{1 + \cfrac{1}{4 + \cfrac{1}{4 + \cfrac{1}{2}}}}.

 May 8, 2024
 #1
avatar+1616 
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This expression is a nested fraction. We can simplify it by working our way from the innermost level outward.

Innermost Level:

21​=0.5

Second Level:

4+0.51​=4.51​=92​

Third Level:

4+92​1​=936+2​1​=938​1​=389​

Outermost Level:

1+389​1​=3838+9​1​=3847​1​=4738​​

Therefore, the value of the expression is 4738​.

 May 9, 2024

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