- #1
darewinder
- 14
- 0
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 isn't a coincedience
Homework Equations
I put the steps into an equation, but i can't prove it.
ln(x) =[tex]^{lim }_{n->inf}[/tex] [tex](x^\frac{1} {2^n} -1)*2^n[/tex]
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 can't get to a form where it is 0/0. I tried factoring, rationalizing but i couldn't 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 that's like the same thing. So if you guys can give me some ideas it would be great! :)
Thank you
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