Taylor/Maclaurin Series Expansion -Σ a-x)" -Σ(+k=1)x* (1-x)-" k=0 for x ER In(1 + x) = [(−1)²+1² k=1 for x € (-1,1) for x € (-1,1]
Taylor/Maclaurin Series Expansion -Σ a-x)" -Σ(+k=1)x* (1-x)-" k=0 for x ER In(1 + x) = [(−1)²+1² k=1 for x € (-1,1) for x € (-1,1]
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![Binomial Theorem
Let a, b E R and n be a nonnegative integer. Then,
72
(a + b)" = [ (1) a"-kbk
k=0
Taylor/Maclaurin Series Expansion
k=0
00
k!
00
(n k_
(-x)=E(+-)
k=0
k
xk
k
In(1 + x) = [(-1)*+1²
k=1
for x ER
for x € (-1,1)
for x € (-1,1]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F108f8a6c-2955-46fa-b885-667817ffe50f%2F4ddc8c25-af68-43b3-864d-b53fcddb7141%2F3gvsxil_processed.png&w=3840&q=75)
Transcribed Image Text:Binomial Theorem
Let a, b E R and n be a nonnegative integer. Then,
72
(a + b)" = [ (1) a"-kbk
k=0
Taylor/Maclaurin Series Expansion
k=0
00
k!
00
(n k_
(-x)=E(+-)
k=0
k
xk
k
In(1 + x) = [(-1)*+1²
k=1
for x ER
for x € (-1,1)
for x € (-1,1]
Transcribed Image Text:4. Let n be a nonnegative integer.
Express each sum in closed form (without or ellipsis) by using Binomial
Theorem or Taylor/Maclaurin series expansion:
00k(k-1)(3-*)
kl
b. 2
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