(a) Prove that the last two digits of 2" cannot be 02 and the last three digits cannot be 108.(b) Find all n such that the sum of the digits of 2n is 5.(c) (not to be graded. Also it might be a little bit difficult, don't spend too much time on it) Show that the limit of thesum of the digits of 2" is ∞ as n→∞0.

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Math

Calculus

Prove that the last two digits of 2" cannot be 02 and the last three digits cannot be 108.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter2: Equations And Inequalities

Section2.6: Inequalities

Problem 78E

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Question

(a) Prove that the last two digits of 2" cannot be 02 and the last three digits cannot be 108.
(b) Find all n such that the sum of the digits of 2n is 5.
(c) (not to be graded. Also it might be a little bit difficult, don't spend too much time on it) Show that the limit of the
sum of the digits of 2" is ∞ as n→∞0.

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