Question

\[{0.\dot1\dot0}_\phi\]

Answer 1

???

Answer 2

\[{0.10101010101010101010...}_\phi\]

Answer 3

Isnt it 10/99

Answer 4

base \(\phi\) ? isnt it null, but u using two digits 0,1

Answer 5

try again

Answer 6

what on earth does that mean?

Answer 7

\[\phi^{-1}+\phi^{-3}+\phi^{-5}+\quad ...\]

Answer 8

I think this should reach 1 on the limit to infinity. It's the sum \[\sum_{n=1}^{\infty} \phi ^{1-2n} \]Am I right? I saw that some time ago, but I don't really remember how to prove it. Is it partial sums?

Answer 9

how can you show that sum is equal to one /

Answer 10

I think you have to find a general partial sum formula and apply it to the limit -> infinity, but it's not a easy limit. Like I said, I saw this a long time now, but I think that the limit (from the partial sum formula) is 1 in the end.
Anyway, I will leave this as a tip, I will check back tomorrow and try to come up with something.