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Use the formula for the binomial series: (1 + x)" 1+ mx + m(m-1)2 + m(m–1)--(m–-k+1), + + ... k! m(m–1)---(m-k+1),nt if |x| < 1 1+ Σ k=l° k! 1 to obtain the Maclaurin series for * (1+x)³ 1 – 3x + (-1)*+1(k + 2)' 4! k=2 k! (k + 3)! 1+ 3! k=1 k! 1 1 – 3x +E(-1)*(k + 2)! k! k=2 + 4)! 1– 3x + : k! k=2 Σ (k + 2)! 1+ 3x + k! k=2

Use the formula for the binomial series: (1 + x)" 1+ mx + m(m-1)2 + m(m–1)--(m–-k+1), + + ... k! m(m–1)---(m-k+1),nt if |x| < 1 1+ Σ k=l° k! 1 to obtain the Maclaurin series for * (1+x)³ 1 – 3x + (-1)*+1(k + 2)' 4! k=2 k! (k + 3)! 1+ 3! k=1 k! 1 1 – 3x +E(-1)*(k + 2)! k! k=2 + 4)! 1– 3x + : k! k=2 Σ (k + 2)! 1+ 3x + k! k=2

Advanced Engineering Mathematics
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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Use the formula for the binomial series: mim-1)2 + (1 + x)" 1+ тx + 2! m(m–1)..(m-k+1) k + ... k! o m(m-1)..(m-k+1)k if 1지 < 1 k! 1 to obtain the Maclaurin series for (1 +x)³" 00 (k + 2)! 1- 3x + 4! 2 k! k=2 00 (k + 3)! 1 1 + 3! k=1 k! 00 1 +2 1- 3x + 2! k=2 k! 00 (k- 1- 3x + 2! k=2 k! (k + 2)! 1 + 3x + >. k! k=2
Transcribed Image Text:Use the formula for the binomial series: mim-1)2 + (1 + x)" 1+ тx + 2! m(m–1)..(m-k+1) k + ... k! o m(m-1)..(m-k+1)k if 1지 < 1 k! 1 to obtain the Maclaurin series for (1 +x)³" 00 (k + 2)! 1- 3x + 4! 2 k! k=2 00 (k + 3)! 1 1 + 3! k=1 k! 00 1 +2 1- 3x + 2! k=2 k! 00 (k- 1- 3x + 2! k=2 k! (k + 2)! 1 + 3x + >. k! k=2
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