Let a₁0 be a real number (to be chosen below) and recursively define for n > 2. a. b. Let ai = an = .3 an-1+an-1 3 1. Show that 0 ≤ an ≤ (²)"−¹ for all n € N. Let a1 = 1 again. Show that lim an = 0. n→∞

Let a₁0 be a real number (to be chosen below) and recursively define for n > 2. a. b. Let ai = an = .3 an-1+an-1 3 1. Show that 0 ≤ an ≤ (²)"−¹ for all n € N. Let a1 = 1 again. Show that lim an = 0. n→∞

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.3: Factorization In F [x]

Problem 23E: Let f(x),g(x),h(x)F[x] where f(x) and g(x) are relatively prime. If h(x)f(x), prove that h(x) and...

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Question

Please prove the following step by step with focus on proof writing style

Let a₁0 be a real number (to be chosen below) and recursively define
an-1 + an-1
3
for n ≥ 2.
a.
b.
Let a1 =
Let a1 =
an
n-1
1. Show that 0 ≤ an ≤ (²)"−¹ for all n € N.
1 again. Show that lim an = 0.
n→∞

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