Use the formula for the binomial series: m(m-1)..(m-k+1), (1 + x)" = 1+ mx + m(m-1)2 2! ... m(m-1)..(m-k+1), 1+ E=1 |x| < 1 k! to obtain the Maclaurin series for 1 +x. +E(-1)*+15-11 - 17.--(6k – 7) k! k=2 1+ E(-1*" 11 17.(6k- 7) 6*k! k=1 15.11 17.(6k- 7) 6k k! +x+ k=2 11 · 17..(6k – 7) k 1+ > k! k=1 5- 11-17--(6k – 7)t 6* 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 50E
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Question
Use the formula for the binomial series:
m(m-1)2
1+ mx +
2!
m(m-1).--(m-k+I).
(1 + x)" =
...
m(m-1)..(m-k+1),
1+ E=1
*if
|x| < 1
k!
to obtain the Maclaurin series for 1 +x.
+ E(-1)*+15-11 - 17...(6k – 7)
k!
k=2
1+ E(-1*1
11 17.(6k-7)
6*k!
k=1
E(-1)*+
5 11 17.(6k - 7)
6k k!
+x+
of
k=2
11 - 17..(6k – 7) *
1+ >
k!
k=1
É-15- 11 - 17.-(6k – 7)
6* k!
k=2
-To
Transcribed Image Text:Use the formula for the binomial series: m(m-1)2 1+ mx + 2! m(m-1).--(m-k+I). (1 + x)" = ... m(m-1)..(m-k+1), 1+ E=1 *if |x| < 1 k! to obtain the Maclaurin series for 1 +x. + E(-1)*+15-11 - 17...(6k – 7) k! k=2 1+ E(-1*1 11 17.(6k-7) 6*k! k=1 E(-1)*+ 5 11 17.(6k - 7) 6k k! +x+ of k=2 11 - 17..(6k – 7) * 1+ > k! k=1 É-15- 11 - 17.-(6k – 7) 6* k! k=2 -To
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