Use the formula for the binomial series: (1+x)" = 1+ mx + m(m-1) 21 m(m-1)--(m-k+1). k! + ... + ... + T 1+ 2k=1' m(m-1).(m-k+1)k 1x지 < 1 8. if %3D k! to obtain the Maclaurin series for V1 + x. 1++E-1y2-15 - 23-(8& – 9) , 1 +x+ k! k=2 + S-17:15 · 23..-(8k – 9) , 8k k!. 1 - k=2 1+ E(-1*. 15 23(8k - 9). 8* k! k=1 -+ Σευ 17 15 23.(8k -9) gkk! 1 + k=2 15 23.(8k-9). 1+ k! k=1

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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Question 2
Use the formula for the binomial series:
m(m-1)-(m-k+1)xt + ..
m(m-1)
2!
m(m-1).(m-k+1) if
(1+x)" =
1+ mx +
+ ... +
k!
1+Ek=1
1지 < 1
%3D
k!
to obtain the Maclaurin series for V1+ x.
7-15 23.(8k – 9)
1
1+r+
k!
k=2
7 15 23.(8k - 9)
1 -
8* k!
k=2
15 23.(8k –9)
8* k!
k=1
E-1*+17·15 · 23.(8k – 9)
8* k!
1 +-x +
k=2
15 23.(8k-9)
1+
k!
k=1
Transcribed Image Text:Use the formula for the binomial series: m(m-1)-(m-k+1)xt + .. m(m-1) 2! m(m-1).(m-k+1) if (1+x)" = 1+ mx + + ... + k! 1+Ek=1 1지 < 1 %3D k! to obtain the Maclaurin series for V1+ x. 7-15 23.(8k – 9) 1 1+r+ k! k=2 7 15 23.(8k - 9) 1 - 8* k! k=2 15 23.(8k –9) 8* k! k=1 E-1*+17·15 · 23.(8k – 9) 8* k! 1 +-x + k=2 15 23.(8k-9) 1+ k! k=1
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