Currently in the book on p. 19 (Neural Networks and Learning Machines Third Edition) I see:

Using the binomial expansion for $(1 - wz^{-1})^{-1}$ , we may rewrite it as $\sum_{l=0}^{\infty}w^{l}z^{-l}$. How Simon did that?


1 Answer 1


I suppose, that progression is connected to this rewriting. Hence, first formula is just the sum of an infinite decreasing geometric progression with $1$ as $b_{1}$ and $wz^{-1}$ as q.

  • $\begingroup$ I think so too, but why he needs "binomial expansion" here?! $\endgroup$ Commented Sep 21, 2015 at 10:57
  • $\begingroup$ okay, i'm not sure i did quite understand your question was. $\endgroup$
    – dshulgin
    Commented Sep 21, 2015 at 11:00
  • $\begingroup$ maybe it's just expression to show a way of thinking. $\endgroup$
    – dshulgin
    Commented Sep 21, 2015 at 11:02
  • $\begingroup$ You are correctly understood my question. $\endgroup$ Commented Sep 21, 2015 at 11:05

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.