466 reputation
313
bio website
location
age
visits member for 3 years, 8 months
seen Aug 25 at 19:49

Jul
2
awarded  Curious
Jan
26
awarded  Notable Question
Nov
21
awarded  Popular Question
Sep
15
awarded  Self-Learner
Aug
16
awarded  Popular Question
Mar
1
awarded  Yearling
Mar
1
accepted Generating functions for sum of powers of two
Mar
1
comment Generating functions for sum of powers of two
I flipped a negative sign in the denominator. It is fixed now. Thanks so much for your help!
Mar
1
revised Generating functions for sum of powers of two
added 7 characters in body
Mar
1
comment Generating functions for sum of powers of two
I must have made some mistake. I believe the answer should be $a_n = 2^{n+1} - 2$.
Mar
1
comment Generating functions for sum of powers of two
I have $A(x) = \frac{1}{2x - 1} - \frac{4}{x - 1} - 3$. So I can write it as $A(x) = -3 + \sum (4 - 2^n) x^n$. This is actually the first problem in generating functions I'm doing on my own. I'm not sure where to go from here.
Mar
1
comment Generating functions for sum of powers of two
@wj32 -- I'm trying to learn independently. I'm currently following along in the Analytic Combinatorics class on Coursera, but this is a sequence that I ran into on my own. (Incidentally, this sequence is the expected number of coin flips you need before you get $n$ heads in a row.)
Mar
1
comment Generating functions for sum of powers of two
Thanks @wj32. Where do I go from here?
Mar
1
revised Generating functions for sum of powers of two
added 259 characters in body
Mar
1
asked Generating functions for sum of powers of two
Feb
19
awarded  Popular Question
Jan
15
awarded  Nice Question
Jan
1
accepted Sangaku: Show line segment is perpendicular to diameter of container circle
Dec
28
accepted Expected smallest prime factor
Dec
28
revised chain rule using tree diagram, why does it work?
deleted 988 characters in body