{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

examsamples

# examsamples - Here is a list of questions I have asked on...

This preview shows pages 1–2. Sign up to view the full content.

Here is a list of questions I have asked on previous exams pertaining to topics covered so far in this course as well as some new questions I have created. Note that just because a topic from those sections is not represented here, does not mean it will not be tested on. This list is simply meant to be representative. Solve the following recurrence relation a n = 5 a n - 1 - 6 a n - 2 + (7 - 2 n )2 n - 1 a 0 = 2 a 1 = 1 . Let a n = 4 a n - 1 + 8 a n - 2 + 7 a n - 3 , with a 0 = 0, a 1 = 1, and a 2 = - 1 Find the generating function for a n . Solve a n = 3 a n - 1 - 2 a n - 2 - n 2 n when a 0 = - 2 and a 1 = - 1. Find generating functions for a n and b n , where a 0 = 1, b 0 = 3, and a n = a n - 1 - 3 b n - 1 b n = - a n - 1 + 2 b n - 1 . Find a n for n 2, when a 2 = 4 , a 3 = 5 and a n = a n - 1 + 6 a n - 2 , for n 4. Evaluate the sum 54 i =0 54 - i j =0 54 - j - k k =0 54! i ! j ! k !(54 - i - j - k )! 2 i 3 j ( - 3) 54 - i - j - k Prove that for all n 0, ( n +1) 2 k = n 2 +1 k = n 3 + ( n + 1) 3 . Determine the number of positive integers solutions to x 1 + x 2 + x 3 + x 4 = 17, where x 1 ∈ { 1 , 2 , 3 } , 4 x 2 , 0

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}