1. (20 points) Define the sequence {an} by: 1023, an + 5 an +1' a =...

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1. (20 points) Define the sequence {an} by: 1023, an + 5 an +1' a₁ = an+1 = (a) Show that |an — √5| ≤ = |an the golden ratio. (b) Hence prove rigorously that n> 1. √5 for all n ≥ 2, where = 1.618... is lim an = n→∞ √5. 1. (20 points) Define the sequence {an} by: 1023, an + 5 an +1' a₁ = an+1 = (a) Show that |an — √5| ≤ = |an the golden ratio. (b) Hence prove rigorously that n> 1. √5 for all n ≥ 2, where = 1.618... is lim an = n→∞ √5.

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Step No 1 Given that a 1... View the full answer