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Golden Ratio
​1+1+1+…=?\sqrt{1 + \sqrt{1 + \sqrt{1 + \dots}}} = ?1+1+1+…​​​=?
​
How do we go about solving this problem? Set the value equal to x:
​x=1+1+1+…x = \sqrt{1 + \sqrt{1 + \sqrt{1 + \dots}}}x=1+1+1+…​​​
​
implying
​x2=1+1+1+1+…=1+xx^2 =1 + \sqrt{1 + \sqrt{1 + \sqrt{1 + \dots}}} = 1 + xx2=1+1+1+1+…​​​=1+x
​
Now have a quadratic equation we can solve: x2−x−1=0x^2 - x - 1 =0x2−x−1=0
, implying one solution is
​x=(1+5)/2x = (1 + \sqrt{5}) /2x=(1+5​)/2
, which amazingly is the golden ratio!
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Complex Analysis

Calculus Computations

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