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11.1.43 Determine whether the sequence converges or diverges. Find the limit. an = cos^2(n)/2^n

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Problem 11.1.43 From James Stewart's Single Variable Calculus - Early Transcendentals 7th edition from chapter 11, Inifinite Sequences and Series - Sequences.
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Determine whether the sequence converges or diverges. If it converges, find the limit. an = cos^2(n)/2^n
Enjoy, and I am available for tutoring and private classes! :)
Determine whether the sequence converges or diverges. If it converges, find the limit. an = cos^2(n)/2^n