1) The following questions with sequences will have some relation with the coming sections (11.2 to 11.6): a) Determine if the sequence converges to 0 or not: Зп + 1 In 2n + 5. cos(nT) dn an = bn sin Cn = n· sin n2 5n b) For the following geometric sequence, what are the ratio r? an = 3n+1 .7-n (-2)?n+1 c) Verify that the sequence is decreasing: an = ne-n d) Please compare the following pairs to see which one is greater: 4" 4n 4" 4" 3" + 5" VS 5" + 5" 3" + 5" VS 3" + 3" e) Please list the first 5 terms of the following sequences (begin with n = 1): Зп — 1 2.5· 8..... 3n – 1 bn 3.5.7..... (2n + 1) an 2n +1
1) The following questions with sequences will have some relation with the coming sections (11.2 to 11.6): a) Determine if the sequence converges to 0 or not: Зп + 1 In 2n + 5. cos(nT) dn an = bn sin Cn = n· sin n2 5n b) For the following geometric sequence, what are the ratio r? an = 3n+1 .7-n (-2)?n+1 c) Verify that the sequence is decreasing: an = ne-n d) Please compare the following pairs to see which one is greater: 4" 4n 4" 4" 3" + 5" VS 5" + 5" 3" + 5" VS 3" + 3" e) Please list the first 5 terms of the following sequences (begin with n = 1): Зп — 1 2.5· 8..... 3n – 1 bn 3.5.7..... (2n + 1) an 2n +1
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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week 4 2 of 4
Transcribed Image Text:1) The following questions with sequences will have some relation with the coming sections (11.2 to 11.6):
a) Determine if the sequence converges to 0 or not:
Зп + 1
In
-), bn =
cos(nn)
dn
An
sin
Cn
= n· sin
n2
5"
b) For the following geometric sequence, what are the ratio r? an = 3"+1·7",
br
(-2)2n+1
c) Verify that the sequence is decreasing: an = ne
-n
d) Please compare the following pairs to see which one is greater:
4"
4"
4"
4"
3" + 5"
VS
5" + 5"
3" + 5"
VS
3" + 3"
e) Please list the first 5 terms of the following sequences (begin with n = 1):
2.5· 8 .
bn
3.5-7..... (2n + 1)
Зп — 1
. Зп — 1
An
2n + 1
||
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