Informal proof of product expansion of geometric series
Notes 
:
(1) Convergence for both is when |x| < 1
(2) I did not prove this because it's Twitter and I'm about to head to the beach 
pic.twitter.com/rUrJ8kMPXG
Show this thread
-
-
Thanks. Twitter will use this to make your timeline better. UndoUndo
-
-
-
Sees blackboard with geometric series... exasperated: why hasn’t anyone factored this?! ... walks away
Thanks. Twitter will use this to make your timeline better. UndoUndo
-
-
-
A good proof here (ignoring issues of convergence) is exactly that every positive integer can be expressed uniquely as a finite binary string.
Thanks. Twitter will use this to make your timeline better. UndoUndo
-
-
-
So for every base b we may take prod_k sum_i x^{i b^k}
Thanks. Twitter will use this to make your timeline better. UndoUndo
-
-
-
What
Thanks. Twitter will use this to make your timeline better. UndoUndo
-
-
-
Sum(0+x^k)=Mul(1+x^2^k)
Thanks. Twitter will use this to make your timeline better. UndoUndo
-
-
-
I can't understand this
Thanks. Twitter will use this to make your timeline better. UndoUndo
-
-
-
Thanks. Twitter will use this to make your timeline better. UndoUndo
-
Loading seems to be taking a while.
Twitter may be over capacity or experiencing a momentary hiccup. Try again or visit Twitter Status for more information.