Use the formula for the binomial series: (1+x)™ = 1 + mx + x² + .… + m(m–1) m(m–1).-(m-k+1). k! + ... ... 2! 1+ Ek=1° т(т-1). (m-k+1), k! Sat if |x| < 1 1 to obtain the Maclaurin series for (1 + x)* (k + 4)! 1+ 4! k=1 k! 1– 4x + k! k=2 1+ 4x + «+ 3)! k! k=2 E(-1)*e+1 (k + 3)', 5! k=2 1 1- 4x + k! 1– 4x + (-1*k + 3)! 3! k=2 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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Use the formula for the binomial series:
m(m–1) 2
(1 + x)" =
m(m–1).….(m-k+1),
k!
1+ mx +
x +
2!
...
...
1+ 5: m(m-1).·(m-k+1) ,k if Ixl < 1
k!
1
to obtain the Maclaurin series for
(1 + x)*
(k + 4)!
1+
4!
k=1
Σ
k!
1– 4x +
3!
(k + 5)!
(-1)*
k!
k=2
(k + 3)!
1+ 4x + >,
k!
k=2
1
1- 4x +
2(-1)*+1 (k + 3)!
5!
k=2
k!
1
- (k + 3)!
(-1)*
3!
k=2
1- 4x +
k!
Transcribed Image Text:View Policies Current Attempt in Progress Use the formula for the binomial series: m(m–1) 2 (1 + x)" = m(m–1).….(m-k+1), k! 1+ mx + x + 2! ... ... 1+ 5: m(m-1).·(m-k+1) ,k if Ixl < 1 k! 1 to obtain the Maclaurin series for (1 + x)* (k + 4)! 1+ 4! k=1 Σ k! 1– 4x + 3! (k + 5)! (-1)* k! k=2 (k + 3)! 1+ 4x + >, k! k=2 1 1- 4x + 2(-1)*+1 (k + 3)! 5! k=2 k! 1 - (k + 3)! (-1)* 3! k=2 1- 4x + k!
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