Use the formula for the binomial series: (1 + x)" m(m–1) 2 -x² + 2! m(m–1)..(m-k+1) + 1+ mx + ... ... k! 1+ Ek=1° * m(m-1).…(m-k+1), 1지 < 1 k! to obtain the Maclaurin series for V1 + x. 5. 8..(3k – 4) 1+ > k! k=1 2.5.8.(3k – 4) 3* + £(-1* 3*k! k=2 + E(-1)*+12· 5 · 8.…(3k – 4) 3* k! k=2 1+ E(-1x3- 8.(3k – 4) 3k k! k=1 1 1 + + E(-1y*+12·5 · 8.--(3k – 4). k! k=2
Use the formula for the binomial series: (1 + x)" m(m–1) 2 -x² + 2! m(m–1)..(m-k+1) + 1+ mx + ... ... k! 1+ Ek=1° * m(m-1).…(m-k+1), 1지 < 1 k! to obtain the Maclaurin series for V1 + x. 5. 8..(3k – 4) 1+ > k! k=1 2.5.8.(3k – 4) 3* + £(-1* 3*k! k=2 + E(-1)*+12· 5 · 8.…(3k – 4) 3* k! k=2 1+ E(-1x3- 8.(3k – 4) 3k k! k=1 1 1 + + E(-1y*+12·5 · 8.--(3k – 4). k! k=2
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 49E
Related questions
Question
![Use the formula for the binomial series:
(1 + x)"
1+ mx +
2!
m(m-1)2 +
m(m-1).(m-k+1),
+
...
...
k!
m(m–1).-(m-k+1) k if
1+ 2k=1°
|지 < 1
k!
to obtain the Maclaurin series for V1 + x.
5. 8...(3k – 4)
1+ E
Σ
k!
k=1
5. 8...(3k – 4)
00
1
3 Σ-1)
3k k!
k=2
+ + E(-1)*+12· 5 . 8...(3k – 4)
3k k!
1
k=2
00
5.8.(3k – 4)
1+ E(-1)2
3* k!
-
k=1
1
1 +
+ E(-1*+12· 5 · 8.…(3k – 4)
k!
k=2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc332f245-233e-4413-8ac6-75dfae80a1d6%2Fb4b201ab-57a0-4687-985a-0a5712061c80%2Fuvkxmvw_processed.png&w=3840&q=75)
Transcribed Image Text:Use the formula for the binomial series:
(1 + x)"
1+ mx +
2!
m(m-1)2 +
m(m-1).(m-k+1),
+
...
...
k!
m(m–1).-(m-k+1) k if
1+ 2k=1°
|지 < 1
k!
to obtain the Maclaurin series for V1 + x.
5. 8...(3k – 4)
1+ E
Σ
k!
k=1
5. 8...(3k – 4)
00
1
3 Σ-1)
3k k!
k=2
+ + E(-1)*+12· 5 . 8...(3k – 4)
3k k!
1
k=2
00
5.8.(3k – 4)
1+ E(-1)2
3* k!
-
k=1
1
1 +
+ E(-1*+12· 5 · 8.…(3k – 4)
k!
k=2
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