If (n + 1)(n + 2)an+1x" - nan-1x" = 0, n=1 show that for k = 1, 2, 3, ..., we have 1.3.5... (2k - 1) ao, 2k+1 k! a1. (2k + 2)! a2k a2k+1 = (2k + 1)!

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.6: Permutations
Problem 12E
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If
(n + 1)(n + 2)an+1x" - nan-1x" = 0,
n=1
show that for k = 1, 2, 3, ..., we have
1.3.5... (2k - 1)
ao,
2k+1 k!
a1.
(2k + 2)!
a2k
a2k+1 =
(2k + 1)!
Transcribed Image Text:If (n + 1)(n + 2)an+1x" - nan-1x" = 0, n=1 show that for k = 1, 2, 3, ..., we have 1.3.5... (2k - 1) ao, 2k+1 k! a1. (2k + 2)! a2k a2k+1 = (2k + 1)!
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