Consider the number C(n,r) given by n! C(n, r) = (2.1) (n – r) ! -r ! where n and r are integers satisfying n 2 2 and n 2 r 2 0 (0! = 1). In particular, C(n, 0) = C(n, n) = 1. ( 2.2) [ You are not required to show ( 2.2).] Let P, := II C(n, k) = C(n, 0)xC(n, 1) × ·… x C(n, n) k- 1 ... for n = 2, 3, .... Does the following limit { Pn + 1 × P, lim exist ? (2.3) You are not required to prove your answer Moreover, if your answer is “Yes", then find the limit , and write down your answer in terms of some of the fundamental numbers like 7, e (base for the natural log . ), 1, 2, .. (note that not all of these number may be present ). Here you are required to justify your answer (on the value of the limit ) . You may take the following limit ) - lim 1 + = e (2.4) for granted [ that is, you are not required to show (2.4)].
Consider the number C(n,r) given by n! C(n, r) = (2.1) (n – r) ! -r ! where n and r are integers satisfying n 2 2 and n 2 r 2 0 (0! = 1). In particular, C(n, 0) = C(n, n) = 1. ( 2.2) [ You are not required to show ( 2.2).] Let P, := II C(n, k) = C(n, 0)xC(n, 1) × ·… x C(n, n) k- 1 ... for n = 2, 3, .... Does the following limit { Pn + 1 × P, lim exist ? (2.3) You are not required to prove your answer Moreover, if your answer is “Yes", then find the limit , and write down your answer in terms of some of the fundamental numbers like 7, e (base for the natural log . ), 1, 2, .. (note that not all of these number may be present ). Here you are required to justify your answer (on the value of the limit ) . You may take the following limit ) - lim 1 + = e (2.4) for granted [ that is, you are not required to show (2.4)].
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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please send solution step by step Q2
![Question 2
Consider the number C(n, r) given by
n!
C(n,r)
(2.1)
(n – r) !·r !
where n and r are integers satisfying
n 2 2
and
n 2r 2 0 ( 0! = 1).
In particular,
С (п, 0)
[ You are not required to show (2.2).] Let
С (п, п) 3D 1.
(2.2)
P, :=
П С(п, К)
C (n, 0) x C (n, 1)× ... x C (n, n)
k = 1
for n
2, 3,
Does the following limit
.....
{
Pn + 1 x Pn - 1
[Pn ]?
lim
n + 00
exist ?
( 2.3)
You are not required to prove your answer
Moreover, if your answer is “Yes", then find the limit, and write down your answer
in terms of some of the fundamental numbers like 7, e (base for the natural log .),
1, 2, ... (note that not all of these number may be present ). Here you are required
to justify your answer (on the value of the limit ). You may take the following limit
lim (1
+ ) -
= e
(2.4)
for granted [ that is, you are not required to show (2.4)].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1dd3f1d5-a48a-4027-93ad-81a55ded7dc8%2F6b1d324a-37cd-4583-838b-4024447c28c5%2Fryvk87_processed.png&w=3840&q=75)
Transcribed Image Text:Question 2
Consider the number C(n, r) given by
n!
C(n,r)
(2.1)
(n – r) !·r !
where n and r are integers satisfying
n 2 2
and
n 2r 2 0 ( 0! = 1).
In particular,
С (п, 0)
[ You are not required to show (2.2).] Let
С (п, п) 3D 1.
(2.2)
P, :=
П С(п, К)
C (n, 0) x C (n, 1)× ... x C (n, n)
k = 1
for n
2, 3,
Does the following limit
.....
{
Pn + 1 x Pn - 1
[Pn ]?
lim
n + 00
exist ?
( 2.3)
You are not required to prove your answer
Moreover, if your answer is “Yes", then find the limit, and write down your answer
in terms of some of the fundamental numbers like 7, e (base for the natural log .),
1, 2, ... (note that not all of these number may be present ). Here you are required
to justify your answer (on the value of the limit ). You may take the following limit
lim (1
+ ) -
= e
(2.4)
for granted [ that is, you are not required to show (2.4)].
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