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Let bo, b,, b,, ... be defined by the formula b, = 4" for every integer n 2 0. Fill in the blanks to show that bo, b,, b, ... satisfies the recurrence relation b, = 4b,-1 for every integer k 2 1. Let k be any integer with k 2 1. Substitute k and k - 1 in place of n, and apply the definition of bor b,, b2, ... to both b, and b,-1. The result is b, = 4* (*) and bk - 1 = (**) for every integer k z 1. It follows that for every integer k 2 1, 4bk -1 = by substitution from L(**) V by basic algebra by substitution from (*) V Thus, bo, b1, b2' satisfies the given recurrence relation. Need Help? Read It

Let bo, b,, b,, ... be defined by the formula b, = 4" for every integer n 2 0. Fill in the blanks to show that bo, b,, b, ... satisfies the recurrence relation b, = 4b,-1 for every integer k 2 1. Let k be any integer with k 2 1. Substitute k and k - 1 in place of n, and apply the definition of bor b,, b2, ... to both b, and b,-1. The result is b, = 4* (*) and bk - 1 = (**) for every integer k z 1. It follows that for every integer k 2 1, 4bk -1 = by substitution from L(**) V by basic algebra by substitution from (*) V Thus, bo, b1, b2' satisfies the given recurrence relation. Need Help? Read It

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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Let bo, b, b,, ... be defined by the formula b, = 4" for every integer n 2 0. Fill in the blanks to show that bo, b,, b,, ... satisfies the recurrence relation b, = 4b,- 1 for every integer k 2 1. Let k be any integer with k 2 1. Substitute k and k - 1 in place of n, and apply the definition of bo, b,, b,, ... to both b, and b,-1: The result is b, = 4* (*) and bk - 1 = (**) for every integer k 2 1. It follows that for every integer k 2 1, = 4 4bk - 1 by substitution from (*) V by basic algebra by substitution from (*) Thus, bo, b,, b2, ... satisfies the given recurrence relation. Need Help? Read It
Transcribed Image Text:Let bo, b, b,, ... be defined by the formula b, = 4" for every integer n 2 0. Fill in the blanks to show that bo, b,, b,, ... satisfies the recurrence relation b, = 4b,- 1 for every integer k 2 1. Let k be any integer with k 2 1. Substitute k and k - 1 in place of n, and apply the definition of bo, b,, b,, ... to both b, and b,-1: The result is b, = 4* (*) and bk - 1 = (**) for every integer k 2 1. It follows that for every integer k 2 1, = 4 4bk - 1 by substitution from (*) V by basic algebra by substitution from (*) Thus, bo, b,, b2, ... satisfies the given recurrence relation. Need Help? Read It
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