Recent content by Sarina3003

Thank you. I have checked my calculation by hand and plug in a0,a1 and a2 and verify that it works now! Thanks for your sheets I have learned some codes in Maple as well and it would be useful when I encounter it in the near future. Thanks again :):)

Thanks for pointing out. I have used Mathematica and typed straight in a[n] and solve it with boundary conditions and it gave me the answer include exponential which i have not seen along the way finding its solution including particular solutions . Have you seen something like that in Maple...

Also, do you have any idea for b). I got the answer for a) now, thanks to you, it looks little bit different from the identity in b) and so i guess i have to do a little bit of work to somehow use the answer from a) and arrive to the identity but since this is power series it is more little...

a0 =130, a1=215, a2=260, here they are. If you have some time, please also help me to check it whether i got it right or wrong, just by the way. Thank you :D

Thanks so much. Yes i know a1, a2 and a0 but i used it to get GF of an. But how is it helpful in this question?

Thanks for that. Should i take the sums of both sides and see what happens? I’m not sure if it is ok since this is a sequence

Homework Statement a) I have to find and expression for sequence of $b_n$ in terms of generating functions of the sequence of $a_n$ $$b_n = (-1)^{n}(n+1)a_0 +(-1)^{n-1}n a_1+...+(-1)2a_{n-1}+a_n$$ with $$a_n = a_{n-1} +8a_{n-2} -12a_{n-3} +25(-3)^{n-2} + 32n^2 -64$$ b) I have to use the...

I got 1) 1 2 2 3 2) 1 1 2 3 3) 1 2 3 3 The first one has 1 way to choose, second has 2, third has 2 and last has 1. Finally it should be 4 :(. I then stuck again. I might get wrong somewhere

Thanks for your reply I have written that increasing with repetition allowed, so this literally mean “weakly increasing”

Hi, Thanks for your reply The reason for the answer in my part a) is because i think each of the digit can have 3 ways of choosing. I know it looks not ok but this is what i had to put down in my test paper The reason i said for the stars and bars method is that i realized it shortly after, when...

Homework Statement The question is counting how many sequence length 10 with 1,2,3 if a) increasing from left to right with repetition allowed b) increase from left to right with each number appear at least once (still with repetition allowed) Homework Equations It is the stars and bars...

Homework Statement Homework Equations All needed are in the picture above (i hope so) The Attempt at a Solution to me it is extremely difficult because it is so complicated with many notations. Also, I actually don't know how to read the question properly to answer it Is E(beta) is the...

For number 2# its not from the book I've been dealing but in the past papers exam of the college!

#1 It is actually from the book but when i realize thay i can do like the 2nd way it's the same answer. It's not wrong when no A but B + B but no A +... because i have asked the teacher. And that question is exactly what is said in the book. And then when i see 2#, i see it almost the same but i...

1/ that is how the answer of the book gives and i understand it in thay way 3/ "replacement" part is which i do not know how to deal with