4. Find the value of n; if Pin.4) - 42P(n 2). 5. Simplify the following (a) (b)12C

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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1 4G I.
9 0:19
1. Pascal Triangle for the expansion of (a +b)*.
2. How many letters words can be form using the letters of words,
MISSISSIPPI and JAZAN.
3. Find the number of distinct permutations that can be formed your ID
number.
4. Find the value of n; if P(n,4) = 42P(n 2).
5. Simplify the following (a)
6. Show that () = () +().
(b)12C,
7. Show that C(2n, 2) = 20(n,2) +nº.
8. Determine whether the sequence (a,l is a solution of recurrence
relation
a= 2an-1-an-2. n22, where a, - 2" for every non-negative
integers n.
9. Find the first five terms of the sequence ag-1ta-1. with a, = 1. a- 2,
10.Find an explicit formula for Fibonacci numbers, where the recurrence
relation for
fn = fn-1 + fa-a where fo = 0, h = 1.
Solve the following recurrence relations
(a)
11.
an=la,-1-10a,-a.
(b)
a 2a-1-a-2. with ao = 4, a, = 1.
12.
Find the generating function for the sequence (e*) where a is fixed
constant.
13
Find the generating function for the sequence (: + 3k + 24).
Find the sequence for the generating functionG) - t
14.
(?
Transcribed Image Text:1 4G I. 9 0:19 1. Pascal Triangle for the expansion of (a +b)*. 2. How many letters words can be form using the letters of words, MISSISSIPPI and JAZAN. 3. Find the number of distinct permutations that can be formed your ID number. 4. Find the value of n; if P(n,4) = 42P(n 2). 5. Simplify the following (a) 6. Show that () = () +(). (b)12C, 7. Show that C(2n, 2) = 20(n,2) +nº. 8. Determine whether the sequence (a,l is a solution of recurrence relation a= 2an-1-an-2. n22, where a, - 2" for every non-negative integers n. 9. Find the first five terms of the sequence ag-1ta-1. with a, = 1. a- 2, 10.Find an explicit formula for Fibonacci numbers, where the recurrence relation for fn = fn-1 + fa-a where fo = 0, h = 1. Solve the following recurrence relations (a) 11. an=la,-1-10a,-a. (b) a 2a-1-a-2. with ao = 4, a, = 1. 12. Find the generating function for the sequence (e*) where a is fixed constant. 13 Find the generating function for the sequence (: + 3k + 24). Find the sequence for the generating functionG) - t 14. (?
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