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Use the formula for the binomial series: (1 + x)" = 1+ тx + 2! m(m–1)2 + m(m-1)…(m-k+1) k1.. ... k! m(m-1)..(m-k+1), St if |x| < 1 k! 1 to obtain the Maclaurin series for (1 + x)8 (-1)* k+ 7)! k! 00 1- 8x + - 7! k=2 1+ 8x + k + 7)! k! 00 k=2 1 + 9)! 1 – 8x + (-1)k ( + 7! k=2 k! 1 – 8x + E- 1)*+1 (k + 7)! 9! k=2 k! (k + 8)! 1 + 8! k=1 k!

Use the formula for the binomial series: (1 + x)" = 1+ тx + 2! m(m–1)2 + m(m-1)…(m-k+1) k1.. ... k! m(m-1)..(m-k+1), St if |x| < 1 k! 1 to obtain the Maclaurin series for (1 + x)8 (-1)* k+ 7)! k! 00 1- 8x + - 7! k=2 1+ 8x + k + 7)! k! 00 k=2 1 + 9)! 1 – 8x + (-1)k ( + 7! k=2 k! 1 – 8x + E- 1)*+1 (k + 7)! 9! k=2 k! (k + 8)! 1 + 8! k=1 k!

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: Kindly provide a clear solution 

Use the formula for the binomial series: (1 + x)" = 1+ тx + 2! m(m–1)2 + m(m-1)…(m-k+1) k1.. ... k! m(m-1)..(m-k+1), St if |x| < 1 k! 1 to obtain the Maclaurin series for (1 + x)8 (-1)* k+ 7)! k! 00 1- 8x + - 7! k=2 1+ 8x + k + 7)! k! 00 k=2 1 + 9)! 1 – 8x + (-1)k ( + 7! k=2 k! 1 – 8x + E- 1)*+1 (k + 7)! 9! k=2 k! (k + 8)! 1 + 8! k=1 k!
Transcribed Image Text:Use the formula for the binomial series: (1 + x)" = 1+ тx + 2! m(m–1)2 + m(m-1)…(m-k+1) k1.. ... k! m(m-1)..(m-k+1), St if |x| < 1 k! 1 to obtain the Maclaurin series for (1 + x)8 (-1)* k+ 7)! k! 00 1- 8x + - 7! k=2 1+ 8x + k + 7)! k! 00 k=2 1 + 9)! 1 – 8x + (-1)k ( + 7! k=2 k! 1 – 8x + E- 1)*+1 (k + 7)! 9! k=2 k! (k + 8)! 1 + 8! k=1 k!
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