-1)k+12 11 17.-(6k – 7) Use the formula for the binomial series: (1+ x)" = m(m-1)2 t … + m(m-1)(m-k+1) 1+ тх + k! 2! 1+ Ek=1 m(m-1)(m-k+1) t if |x| < 1 k! to obtain the Maclaurin series for V1 + x. 1 1+-x+ 9. 5- 11 - 17.-(6k – 7) 6* k! k=2 E(-12 11 17..-(6k – 7) 6* k! CO 1 1--x+ 6. k=2 1 + (-1)1 17.--(6k – 7) 6'k! k=1 11 - 17..(6k – 7). 1+ k! k=1 1 1+-x + k!

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 44E
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Question
Q2
Use the formula for the binomial series:
m(m-1)-(m-k+1)
(1+ x)" =
m(m-1)
2!
1+ mx +
k!
m(m-1).(m-k+1)
k=1
|x| < 1
1+ E
if
k!
to obtain the Maclaurin series for 1+ x.
5- 11 - 17.--(6k – 7)
6* k!
00
1
1+-x+
'일
k=2
1
1–-x+
E-1 11 · 17.--(6k – 7)
6'k!
k=2
11 - 17.--(6k – 7).
6*k!
1 +
k=1
11 - 17.(6k – 7).
1+ >
k!
k=1
1
1+x+
-1*+1211 - 17.--(6k – 7)
k!
k=2
-To
Transcribed Image Text:Use the formula for the binomial series: m(m-1)-(m-k+1) (1+ x)" = m(m-1) 2! 1+ mx + k! m(m-1).(m-k+1) k=1 |x| < 1 1+ E if k! to obtain the Maclaurin series for 1+ x. 5- 11 - 17.--(6k – 7) 6* k! 00 1 1+-x+ '일 k=2 1 1–-x+ E-1 11 · 17.--(6k – 7) 6'k! k=2 11 - 17.--(6k – 7). 6*k! 1 + k=1 11 - 17.(6k – 7). 1+ > k! k=1 1 1+x+ -1*+1211 - 17.--(6k – 7) k! k=2 -To
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