Let {un}, n ≥ 0, be a sequence defined inductively and un+1 = 3un + 3n for n ≥ 0. Then un n3n-1 for all n ≥ 0. as follows: up = 0, =

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section: Chapter Questions
Problem 8RE
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8.
ignment
Let {un}, n ≥ 0, be a sequence defined inductively as follows: uo = 0,
and Un+1 =
3un + 3n for n ≥ 0. Then un = n3n-1 for all n ≥ 0.
We use induction on n
we
For n=0 no = Ox 301=0
Assome un = n3^¹, then un+1=3 un +3^ = 3n 3^² +3^ = n3" + 3" =
Hence
by induction, result holds
Transcribed Image Text:8. ignment Let {un}, n ≥ 0, be a sequence defined inductively as follows: uo = 0, and Un+1 = 3un + 3n for n ≥ 0. Then un = n3n-1 for all n ≥ 0. We use induction on n we For n=0 no = Ox 301=0 Assome un = n3^¹, then un+1=3 un +3^ = 3n 3^² +3^ = n3" + 3" = Hence by induction, result holds
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