I have some questions which are needed to be completed by tomorrow.
Some of them i am going to post here.
Kindly message me if you are able to complete this project on time.
1. Let {fn : n = 0,1,...} be the Fibonacci sequence (where by convention f0 = 0 and f1 = 1).
(a) Prove that
∞
nfn =20 n=1 2n−1
Do this by using a generating function as shown in the last section of the Lecture 2 notes, and differentiating.
(b) Show why (in the same way as you proved the first part of this problem) you might think that
∞
nfn = 2 n=1
Then show why it could not possibly be true.
2. Prove that for positive integers a, b, and n,
n a b = a+b k=0 k n−k n
Use the following facts in your proof: (a)
(1+x)a(1+x)b =(1+x)a+b
(b) You may find it convenient at some point to remember that if m and j are integers (and m ≥ 0), then
mj = 0 i f j < 0 o r j > m
3. Decide whether each of the following statements is true or false, and prove that your conclusion is correct.
• n2 = O(2n)
• 2n+1 = O(2n)
• 22n = O(2n)
• f(n) = O g(n) implies 2f(n) = O 2g(n)
4. Provethatlogax=O(logbx)foranya>1andb>1.
Do this by using a generating function as shown in the last section of the Lecture 2 notes, and differentiating.
need further elaboration on this part .
I am a very good programmer and love to solve algorithmic problems. You can view my linkedin page from my profile. Also you can google "adi_prakash spoj" and find out my SPOJ page where I have solved numerous of such types of problems. This why I think your top choice should be me.
Also presently I am on a leave from my job, So you will have all my time. Hope to talk to you soon.