Consider the following sequence, un+1 = log2 (n +1+ un) for n EN' where u1 = 1. Show that for each n EN', un+1 > un. You can use without proof the fact that the function log2(x) is an increasing function when x 21 (i.e., if x>x' 2 1, log2(x) > log2(x')).
Consider the following sequence, un+1 = log2 (n +1+ un) for n EN' where u1 = 1. Show that for each n EN', un+1 > un. You can use without proof the fact that the function log2(x) is an increasing function when x 21 (i.e., if x>x' 2 1, log2(x) > log2(x')).
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter7: Exponents And Exponential Functions
Section7.8: Transforming Exponential Expressions
Problem 1CYU
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![Consider the following sequence, un+1 = log2 (n +1+ un) for n EN where u1 = 1. Show
that for each n E N", un+1 > un. You can use without proof the fact that the function
log2(x) is an increasing function when x 21 (i.e., if x > x' 2 1, log2(x) > log2(x')).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4294d510-0458-4794-a3cd-a062d110c35a%2F22c096b4-6214-447e-a3ea-848ba88cc797%2Fjrls5h_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the following sequence, un+1 = log2 (n +1+ un) for n EN where u1 = 1. Show
that for each n E N", un+1 > un. You can use without proof the fact that the function
log2(x) is an increasing function when x 21 (i.e., if x > x' 2 1, log2(x) > log2(x')).
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