Use (1 + x)" =1+ Σ k=1 Maclaurin series for (a) (b) (c) 1 1+x √1 1+x (1+x) ³ m(m-1)... (m-k+1)* if |x| <1, to obtain the k!
Use (1 + x)" =1+ Σ k=1 Maclaurin series for (a) (b) (c) 1 1+x √1 1+x (1+x) ³ m(m-1)... (m-k+1)* if |x| <1, to obtain the k!
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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![To obtain the Maclaurin series for the following functions, use the formula:
\[
(1+x)^m = 1 + \sum_{k=1}^{\infty} \frac{m(m-1)\cdots(m-k+1)}{k!} x^k
\]
This formula is valid for \(|x| < 1\).
### Maclaurin Series for:
#### (a) \(\frac{1}{1+x}\)
#### (b) \(\sqrt[3]{1+x}\)
#### (c) \(\frac{1}{(1+x)^3}\)
Each of these functions can be expanded using the given formula to find their respective series representations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F80f7a2c1-bbd9-492a-a9a7-34302e2af2a3%2F27705053-f983-4e8f-97c3-898106a202b8%2F76kl90q_processed.jpeg&w=3840&q=75)
Transcribed Image Text:To obtain the Maclaurin series for the following functions, use the formula:
\[
(1+x)^m = 1 + \sum_{k=1}^{\infty} \frac{m(m-1)\cdots(m-k+1)}{k!} x^k
\]
This formula is valid for \(|x| < 1\).
### Maclaurin Series for:
#### (a) \(\frac{1}{1+x}\)
#### (b) \(\sqrt[3]{1+x}\)
#### (c) \(\frac{1}{(1+x)^3}\)
Each of these functions can be expanded using the given formula to find their respective series representations.
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