The coefficient of k-1 in 1+x (1-2x)5
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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Question
#4 and 5
![EXERCISES 7.2.7. Calculate the following.
2) The coefficient of x4 in (1-x)-².
3) The coefficient of an in (1+x)-4.
4) The coefficient of x-1 in
=
1+x
(1-2x)5
[Hint: Notice that
(1-2x)-5+ (1 - 2r)-5. Work out the coefficient of an in
(1-2x)-5 and in x(1-2x)-5, substitute n = k-1, and add the two coefficients.]
5) The coefficient of rk in 1/(1-¹)", where j and n are fixed positive integers.
[Hint: Think about what conditions will make this coefficient zero.]
200](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F718b1378-40e4-4c32-83bc-211fc46d7de4%2F04ed8fbb-10a9-4127-b4d5-d99fd5525210%2Fc7v3q3_processed.jpeg&w=3840&q=75)
Transcribed Image Text:EXERCISES 7.2.7. Calculate the following.
2) The coefficient of x4 in (1-x)-².
3) The coefficient of an in (1+x)-4.
4) The coefficient of x-1 in
=
1+x
(1-2x)5
[Hint: Notice that
(1-2x)-5+ (1 - 2r)-5. Work out the coefficient of an in
(1-2x)-5 and in x(1-2x)-5, substitute n = k-1, and add the two coefficients.]
5) The coefficient of rk in 1/(1-¹)", where j and n are fixed positive integers.
[Hint: Think about what conditions will make this coefficient zero.]
200
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