Use the formula for the binomial series: m(m-1) m(m-1).(m-k+1), (1 + x)" 1+ mx + x² + 2! ... ... k! 1+ 2k=1 m(m-1)..(m-k+1) x if |지 < 1 k! to obtain the Maclaurin series for V1 + x. 1 1 + r+ E(-1)*+16· 13 · 20--(7k – 8) k! k=2 1+ E(-113 · 20(7k – 8) 7kk! k=1 r + E(-1)*+16 · 13 · 20-(7k – 8) 7k k! 00 1+r+ > k=2 00 1 6. 13 · 20..(7k – 8) 7* k! k=2 13 · 20..(7k – 8) 1+ 2: 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
Use the formula for the binomial series:
(1 + x)" =
m(m-1).
1+ mx +
2!
m(m–1).--(m-k+1).
+
...
...
k!
1+ 2k=1
m(m–1).--(m-k+1)_k if
|x| < 1
k!
to obtain the Maclaurin series for V1 + x.
1
Σ
..
1+r+ (-1)*+16 · 13 · 20…(7k – 8)
k!
k=2
13· 20..(7k – 8)
1+ E(-1)*.
7k k!
k=1
E(-1)k+16: 13 -· 20-(7k – 8)
7k k!
00
1
1+=x +
Σ
k=2
E(-16: 13 · 20-…(7k – 8)
7k k!
k=2
13 · 20..(7k – 8)
Σ
1 +
k!
k=1
Transcribed Image Text:Use the formula for the binomial series: (1 + x)" = m(m-1). 1+ mx + 2! m(m–1).--(m-k+1). + ... ... k! 1+ 2k=1 m(m–1).--(m-k+1)_k if |x| < 1 k! to obtain the Maclaurin series for V1 + x. 1 Σ .. 1+r+ (-1)*+16 · 13 · 20…(7k – 8) k! k=2 13· 20..(7k – 8) 1+ E(-1)*. 7k k! k=1 E(-1)k+16: 13 -· 20-(7k – 8) 7k k! 00 1 1+=x + Σ k=2 E(-16: 13 · 20-…(7k – 8) 7k k! k=2 13 · 20..(7k – 8) Σ 1 + k! k=1
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