(a) Find a formula for the general term an of the sequence 8 3 4 4' 9 - } assuming that the pattern of the first few terms continues. (b) Find the limit of the sequence 2πη2 + en 3n² - ле - 5 6 16 25 + 3n (-1)³n 3n } if it converges. Otherwise, state that the sequence diverges. (c) Find the limit of the sequence {In(5n³ − n + 1) − In(7n³ − n + 1)} - if it converges. Otherwise, state that the sequence diverges. (d) Find the limit of the sequence In(3n²) In(8m) } if it converges. Otherwise, state that the sequence diverges.
(a) Find a formula for the general term an of the sequence 8 3 4 4' 9 - } assuming that the pattern of the first few terms continues. (b) Find the limit of the sequence 2πη2 + en 3n² - ле - 5 6 16 25 + 3n (-1)³n 3n } if it converges. Otherwise, state that the sequence diverges. (c) Find the limit of the sequence {In(5n³ − n + 1) − In(7n³ − n + 1)} - if it converges. Otherwise, state that the sequence diverges. (d) Find the limit of the sequence In(3n²) In(8m) } if it converges. Otherwise, state that the sequence diverges.
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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![(a) Find a formula for the general term
an
of the sequence
2
3
4
5 6
9
4' 9' 16' 25
, assuming that the pattern of the first few terms continues.
(b) Find the limit of the sequence
2πη2 + eπ
(-1)3n
3n² ле
3n
·}
+
if it converges. Otherwise, state that the sequence diverges.
(c) Find the limit of the sequence
{In(5n³ − n + 1) − ln(7n³ − n + 1)}
In(3n²)
In(8n)
if it converges. Otherwise, state that the sequence diverges.
(d) Find the limit of the sequence
{!
if it converges. Otherwise, state that the sequence diverges.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3f0da5ef-7e46-454f-bc98-b8a536ed042b%2F162baa8a-26a2-43aa-a1b0-aff2e5101f75%2Flxbta77_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(a) Find a formula for the general term
an
of the sequence
2
3
4
5 6
9
4' 9' 16' 25
, assuming that the pattern of the first few terms continues.
(b) Find the limit of the sequence
2πη2 + eπ
(-1)3n
3n² ле
3n
·}
+
if it converges. Otherwise, state that the sequence diverges.
(c) Find the limit of the sequence
{In(5n³ − n + 1) − ln(7n³ − n + 1)}
In(3n²)
In(8n)
if it converges. Otherwise, state that the sequence diverges.
(d) Find the limit of the sequence
{!
if it converges. Otherwise, state that the sequence diverges.
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