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**1. Homework Statement**

Well we are given a series of steps done with the number "x" and in the end the end value is ln(x). Basically we are asked to prove why it isnt a coincedience

**2. Homework Equations**

I put the steps into an equation, but i cant prove it.

ln(x) =[tex]^{lim }_{n->inf}[/tex] [tex](x^\frac{1} {2^n} -1)*2^n[/tex]

**3. The Attempt at a Solution**

Well plugging in gives me inf times 0 so i thought of solving it using Hopital's rule but i cant get to a form where it is 0/0. I tried factoring, rationalizing but i couldnt get anywhere. I would appreciate if you guys can help me do this little bit.

and I would also appreciate if anyone can show me how to come up with a sequence for this. Second part of the question askes me to come up with my own limit of a sequence to get ln(x). I just flipped changed the sine of - inside the brackets to make it + and added the minus sign to the -2n at the end, but thats like the same thing. So if you guys can give me some ideas it would be great!! :)

Thank you

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