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Use the formula for the binomial series: to obtain the Maclaurin series for 1 + 3x + Σ (k+2)! k! 00 1 + 1- 3x + + 12/17 (-1)^(k+ 2)! k! 21 k=2 1 1 - 3x + (-1) (k+4)! 2! xk k! (1 + x) = = k=2 1 - 3x + / / 2 (-1)^²+1 (k+ + * 4! k=2 k! (k + 3)! LI 1 (1+x) ³¹ xk (k+2)! = 1 + mx + 1+ Σκι m(m-1), 2 2! ²x² + ... + m(m−1)---(m=k+1) k! m(m-1)-(m=k+1), k! 2xkif x < 1 2

Use the formula for the binomial series: to obtain the Maclaurin series for 1 + 3x + Σ (k+2)! k! 00 1 + 1- 3x + + 12/17 (-1)^(k+ 2)! k! 21 k=2 1 1 - 3x + (-1) (k+4)! 2! xk k! (1 + x) = = k=2 1 - 3x + / / 2 (-1)^²+1 (k+ + * 4! k=2 k! (k + 3)! LI 1 (1+x) ³¹ xk (k+2)! = 1 + mx + 1+ Σκι m(m-1), 2 2! ²x² + ... + m(m−1)---(m=k+1) k! m(m-1)-(m=k+1), k! 2xkif x < 1 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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Question 2 of 9 < Use the formula for the binomial series: (1 + x) to obtain the Maclaurin series for 1+ 3x + Σ k=2 1-3x + 1 - 3x + + 27 (−1)k (k + 2)! k k! k=2 1+ (k+2)! k! 1 - 3x + (−1)k (k+4)! 2! k! 3! 00 k=1 k=2 (−1)k+1 (k+ 2)! 4! k! k=2 1 (1+x)³¹ (k+ 3)! k! = = k 1 + mx + 1+ 2x=1 m(m-1) 2 2! ²x² + + m(m−1)--- (m_k+1), k! mm-1)---(m-k+1) kif k! 2x² + .. < 1 2
Transcribed Image Text:Question 2 of 9 < Use the formula for the binomial series: (1 + x) to obtain the Maclaurin series for 1+ 3x + Σ k=2 1-3x + 1 - 3x + + 27 (−1)k (k + 2)! k k! k=2 1+ (k+2)! k! 1 - 3x + (−1)k (k+4)! 2! k! 3! 00 k=1 k=2 (−1)k+1 (k+ 2)! 4! k! k=2 1 (1+x)³¹ (k+ 3)! k! = = k 1 + mx + 1+ 2x=1 m(m-1) 2 2! ²x² + + m(m−1)--- (m_k+1), k! mm-1)---(m-k+1) kif k! 2x² + .. < 1 2
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